Nama : Ida Ayu Komala Komala Dewi Dewi NIM
: 1304505016
8.1 Uji Validita liditass Cluster Ide!s Ide!s Da"ies#$ouldi
Uji Uji vali validi ditas tas cluster digunakan digunakan untuk mengevaluas mengevaluasii hasil dari analisis analisis cluster secara secara kuanti kuantitati tatiff sehing sehingga ga dihasi dihasilka lkan n kelomp kelompok ok optima optimal. l. Kelom Kelompok pok optimal adalah kelompok yang mempunyai jarak yang padat antar individu dalam kelompok dan terisolasi dari kelompok lain dengan baik (Dubes and Jain, 1!!". #ndeks #ndeks Davies Davies $ouldin $ouldin (D$#" diperkenalk diperkenalkan an oleh David %. Davies dan Donald Donald &. $ouldi $ouldin n pada pada tahun tahun 1', 1', dan diguna digunakan kan untuk untuk mengev mengevalua aluasi si algoritma cluster ing. ing. enggunaan enggunaan indeks indeks validitas validitas Davies)$oul Davies)$ouldin din dapat mengidenti mengidentifikasik fikasikan an cluster yang yang padat (compact ( compact tcluster " dan terpisah dengan baik terhadap terhadap cluster yang lain (Well-Separated (Well-Separated " seperti halnya pada indeks validitas Dunn
ada ada perh erhitun itunga gan n jara jarak k cluster menggu menggunak nakan an #ndeks #ndeks Davies Davies $ouldin $ouldin ini terdapat terdapat * tahap yang digunakan digunakan yaitu perhitungan perhitungan jarak intracluster dan perhitungan jarak intercluster . engukuran dengan metode ini bertujuan untuk memaksimalka memaksimalkan n jarak intercluster antara antara salah salah satu cluster dengan dengan cluster yang lain lain (separ (separati ation on value" value" sekali sekaligus gus memini meminimal malkan kan jarak jarak intracluster antara titik dalam sebuah cluster (compactness (compactness value" ($olshakova ($olshakova + -uaje ** / 0unter 0unter + $unke **". $erikut merupakan contoh penerapan perhitungan indeks Davies)$ouldin pada cluster K)medoids K)medoids dengan data objek seperti pada table !.1. %a&le 8.1 Data bjek Cluster K)medoids K)medoids
data 1 * 4 3 5 6 ' !
2 3 1 1* * 36 41 *1 *!
y 44 15 45 6 1 31 46 4
1 11 1* 14 13 15 16 1' 1! 1 * *1 ** *4 *3 *5 *6 *' *! * 4 41 4* 44 43 45 46 4' 4! 4 3 31 3* 34 33 35 36 3' 3! 3 5
4 36 13 33 31 35 *3 46 15 35 6 * *6 35 36 *6 11 ' 1* 4 * *' ! 35 * *' 33 1 ! *4 1 ** *1 * * 4! 1* 3* 1* 41
*! * *! 11 *3 ! 33 14 1' 4 *! 4' 3! 33 1 *6 33 4 41 46 6 36 44 *1 13 11 ' 14 13 45 3 5 1 3* 4* ' 4! * 33 * 44 1'
erh erhit itun unga gan n jarak jarak pada pada uji uji coba coba inde indeks ks Davi Davies) es)$o $oul uldi din n digu diguna naka kan n perhitungan jarak 7anberra Distance, untuk setiap nilai dari * vektor yang akan dicocokkan dicocokkan,, Canberra distance distance membagi absolute selisih absolute selisih * nilai dengan jumlah dari absolute * nilai tersebut. 8asil dari setiap dua nilai yang dicocokkan lalu dijumlahkan untuk mendapatkan Canberra distance. distance . Jika kedua koordinat nol)nol kita kita memb member erik ikan an defi defini nisi si deng dengan an 9 9 : . Distance Distance ini sangat peka terhadap sedikit sedikit perubahan perubahan dengan kedua koordinat mendekati mendekati nol. ;umus dari Canberra distance< distance<
7ontoh < Untuk vektor dan $ adalah sebagai berikut <
Canberra distance)nya distance )nya adalah <
8.' Uji Validitas Ide!s Da"ies#$ouldi '#cluster
=erdapat data sample yang akan digunakan untuk memvalidasi * cluster yang sudah mengalami proses cluster ing dengan menggunakan algoritma k) medoids, data sample tersebut berisikan titik)titik jarak yang sudah di cluster ing, maka akan dilakukan uji validitas cluster dengan menggunakan indeks Davies $ouldin. Data sample yang akan diuji validitasnya dapat dilihat sebagai berikut.
(am&a) 8.1 Data >ample Untuk ?enghitung Jarak * Cluster Dengan ?enggunakan #ndeks
Davies $ouldin.
0ambar !.1 menunjukkan data sample yang akan digunakan maka data sample tersebut memiliki * cluster sebagai berikut.
%a&el 8.' Data sampel pengujian *)cluster
7luster 1 36 1 41 31 36 * 33 11 31 *3 35 ! 46 1' 35 *! * 3! 35 1 36 33 4 36 35 11 * ' 33 13 * ' 4! *
7luster * 3 44 1* 5 * 6 *1 46 *! 4 4 *! 13 *! 33 *3 14 15 4 6 4' *6 33 *6 *6 4 11 41 ' 46 1* 6
41
*' ! *' 1 ! *4 1 ** *1 * 1* 1*
1'
*1 13 14 45 3 5 1 3* 4* 4! 33 44
8.'.1 *e)+itu,a -a)a! Intracluster '#cluster
>etelah mendapatkan * cluster yang akan diuji maka selanjutnya melakukan perhitungan dengan menggunakan indeks Davies $ouldin. =ahap pertama yang akan dilakukan adalah melakukan perhitungan jarak intracluster dimana perhitungan ini akan menghitung data sample pada masing)masing
cluster . Cluster 1 menghitung anggota data sample yang ada didalamnya dan cluster * juga menghitung anggota data sample yang adadidalammya. erhitungan jarak intracluster ini menggunakan perhitungan jarak dengan matri2 7anberra Distance, maka perhitungannya adalah sebagai berikut. ;umus 7anbbera Distance <
%a&el 8.3 erhitungan Intracluster pada Cluster 1
d@c1
=*
36
1
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d@c1 d@c1
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=abel !.4 merupakan perhitungan pada cluster 1 yang menghitung setiap jarak dari setiap anggota yang ada pada cluster 1, sebagai contoh untuk menghitung jarak dari setiap data sample dengan contoh mengambil pada data sample pertama sebagai berikut. dAc1 : (=1,=*"
B
:
?aka jarak yang didapat dari perhitungan jarak 7anbbera adalah .1 erhitungan untuk mencari jarak intracluster dilakukan sampai data sample pada cluster 1 sudah dihitung sampai habis dari semua data sample yang ada. >elanjutnya menghitung jarak intracluster pada cluster * dapat dilihat sebagai berikut. %a&el 8.4 erhitungan Intracluster pada Cluster *
d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c*
=1
=* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
44 44 44 44 44 44 44 44 44 44 44 44 44 44 44
1* * *1 *! 4 13 *3 15 6 *6 *6 11 '
5 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46
.3! .4 .6! .'5 .13 .55 .4! .' .5! .* .'4 .4! .'4 .3' .*'
d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c*
=*
=4
=1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =3 =5 =6 ='
3 3 3 3 3 3 3 3 3 3 3 3 3 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* * * * *
44 44 44 44 44 44 44 44 44 44 44 44 44 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6
1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* * *1 *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* *1 *! 4 13
6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 46 4 *! *!
.3! .'3 .4* .'4 .6 .44 .' .5 .6 .6! .44 .5 .5 .'1 .*' .4 .5' .' .13 .44 .11 .4* .46 .13 .46 .3 .*5 .4! .* .4! .! .1 .41 .! .* .*' .6! .! .!5 .1! .'*
d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c*
=3
=! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6
* * * * * * * * * * * * * * * * * * * * * * *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1 *1
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46
*3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1
33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4*
.6 .!4 .'4 .36 .!4 .6 .!3 .66 .51 .'1 .!5 .5! .!5 .*' .56 .!1 .*' .!1 .! .6! .6! .13 .'5 .* .3 .' .1' .56 .11 .3 .11 .41 .5 .*' .1* .33 .1* .1 .35 .5 .!' .*
d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c* d@c*
=5
=6
=*' =*! =* =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4
*1 *1 *1 *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
46 46 46 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *!
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=abel !.3 merupakan perhitungan untuk menghitung intracluster jarak pada cluster *, dihitung menggunakan jarak matrik 7anberra, perhitungan yang dilakukan sama seperti pada menghitunga jarak intracluster pada cluster 1. >etelah
melakukan
perhitungan
jarak
intracluster ,
maka
akan
mendapatkan hasil jarak maksimal dari masing)masing cluster . Jarak maksimal yang didapat adalah sebagai berikut. 1. Cluster 1
*. Cluster *
Jarak maksimal yang didapat pada cluster 1 yaitu pada jarak (=1,=3", (=1,16", (=4,=13", (=1,=11" yang memiliki nilai jarak .*4 dan cluster * yaitu pada jarak (=5,=*1" yang memiliki nilai jarak ,4.
8.'.' *e)+itu,a -a)a! Intercluster '#cluster
>etelah melakukan perhitungan jarak intercluster , tahap kedua adalah menghitung jarak intercluster tiap titik pada tiap cluster , dengan menggunakan rumus sebagai berikut.
erhitungan yang dilakukan adalah dengan menghitung data sample yang ada pada cluster 1 dengan data sampel yang ada pada cluster *. erhitungan jarak yang akan dihitung menggunakan perhitungan jarak matrik 7anberra Distance. ada perhitungan jarak intercluster agar perhitungannya terlihat lebih jelas, dapat dilihat perhitungannya sebagai berikut. %a&el 8.5 erhitungan Jarak Intercluster pada Cluster 1 dan Cluster *
d d d d d d d d d d d d d d d d d d d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=1
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=1 =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*!
36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 1* * *1 *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1*
44 5 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33
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d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=*
=4
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =1 =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13
36 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 36 36 36 36 36 36 36 36 36 36 36 36 36 36
1 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 * * * * * * * * * * * * * *
1* 3 1* * *1 *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* 3 1* * *1 *! 4 13 *3 15 6 *6 *6
44 44 5 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 44 5 6 46 4 *! *! 33 14 4 4' 33 *6 4
.5! .'' .34 .!6 .1 .5 .!* .4! .55 .14 .45 .6' . .55 . .3' .64 .34 .' .5! .' .3 .5 .15 .1 .1' .1 .!! .33 .33 .!3 .5! .1 .4' .*3 .!' .54 .6' .41 .51 .'6 .*! .6' .*!
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=3
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =1 =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =*
36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33
* * * * * * * * * * * * * * * 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* 3 1* * *1 *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1*
41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 44 5 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44
.61 .'4 .5! .*6 .' .*6 .5 .' .44 .3 .45 .4' .1 .5! .5! .!* .5' .1 .45 .** .!6 .51 .65 .* .3 .'5 .*5 .66 .*6 .5 .'* .5' .*3 .6 .*3 .3 .6! .41 .3 .44 .45 . .5' .5'
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=1 =* =4 =3 =5 =6 =' =! = =1 =11 =1* =14 =13 =15 =16 =1' =1! =1 =* =*1 =** =*4 =*3 =*5 =*6 =*' =*! =* =1 =* =4 =3 =5 =6 =' =! =
31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 35 35 35 35 35 35 35 35 35
*3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 *3 ! ! ! ! ! ! ! ! !
3 1* * *1 *! 4 13 *3 15 6 *6 *6 11 ' 1* *' ! *' 1 ! *4 1 ** *1 * 1* 1* 3 1* * *1 *! 4 13 *3
44 5 6 46 4 *! *! 33 14 4 4' 33 *6 4 41 46 6 *1 13 14 45 3 5 1 3* 4* 4! 33 44 44 5 6 46 4 *! *! 33 14
.!* .53 .! .4* .1 .!6 .3 .63 .*6 .36 .'3 .** .63 .** .5! .'1 .53 .*1 .6' .* .5 .6' .*! .4 .4 .4* . .53 .55 .!4 .5! .1 .46 .*4 .!6 .5* .66 .4
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4
36
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4
36
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36
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5
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6
.!
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4
36
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46
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c1
c*
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4
36
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.16
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4
36
4
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36
13
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=
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14
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d d
c1 c1
c* c*
=1 =11
4 4
36 36
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=1*
=14
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33
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11
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.56
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d d
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33
13
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13
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5
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33
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33
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d
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.**
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4
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15
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6
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1
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5
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d
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d d
c1 c1
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6 46
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=15
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d
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d
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.
d
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d
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d
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4
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d
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11
41
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d
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d
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d
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d
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d
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1
45
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d
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=**
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d
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5
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d
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d
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44
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.51
d
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4!
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6
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46
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d
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d
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d
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33
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d d
c1 c1
c* c*
=13 =15
4! 4!
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4 41
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=1'
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5
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41
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d
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14
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41
1'
15
4
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d
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41
1'
6
4'
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d
c1
c*
=1*
41
1'
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33
.
d
c1
c*
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41
1'
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.55
d
c1
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41
1'
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4
.
d
c1
c*
=15
41
1'
11
41
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d
c1
c*
=16
41
1'
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46
.64
d
c1
c*
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41
1'
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6
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d
c1
c*
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41
1'
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d
c1
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41
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13
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14
.'
d
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41
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1
45
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3
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=*4
41
1'
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5
.15
d
c1
c*
=*3
41
1'
1
1
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d d
c1 c1
c* c*
=*5 =*6
41 41
1' 1'
** *1
3* 4*
.1' .1
=1!
d
c1
c*
=*'
41
1'
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4!
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d
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41
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33
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d
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44
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=abel !.5 merupakan perhitungan intercluster pada cluster 1 dengan cluster *, sebagai contoh untuk menghitung jarak dari setiap data sample dengan contoh mengambil pada data sample pertama sebagai berikut.
d(c1=1,c*=*" : d((36,1",(3,44""
:
B
?aka jarak yang didapat dari perhitungan jarak 7anbbera adalah .!4 erhitungan untuk mencari jarak intercluster dilakukan sampai data sample pada cluster 1 dengan cluster * sudah dihitung sampai habis dari semua data sample yang ada. >etelah melakukan perhitungan jarak intercluster , maka akan mendapatkan hasil jarak minimal dari tiap data sample dari cluster yang dihitung dapat dilihat sebagai berikut.
8.'.3 *e)+itu,a Ide!s Da"ies $ouldi '#cluster
>elanjutnya setelah melakukan perhitungan kedua jarak yaitu jarak intracluster dan intercluster maka akan melakukan perhitungan dengan indeks Davies $ouldin dengan menggunakan rumus sebagai berikut.
;umus tersebut menjelaskan pada dAc1 dan dAc* masukkan hasil maksimal yang sudah didapat dari perhitungan intracluster . >elanjutnya pada d(ci,c j" masukkan hasil minimum yang sudah didapatkan dari perhitungan intercluster .
Dapat dilihat dengan menggunakan rumus perhitungan dari Davies $ouldin adalah sebagai berikut.
>ehingga akan didapatkan nilai dari indeks Davies $ouldin yang akan dihitung sebagai berikut.
Cilai dari indeks Davies $ouldin yang didapatkan setelah dihitung adalah .5''454'.
8.3 Uji Validitas Ide!s Da"ies#$ouldi 3#cluster
Data sampel yang digunakan pada pengujian validitas indeks Davies) $ouldin pada 4)cluster ditunjukkan pada tabel !.6
%a&el 8.6 Data sample 4)cluster cluster 1
cluster '
cluster 3
3
44
36
1
41
31
4
*!
41
31
6
4'
36
*
1 1*
15 45
*6
33
11
*1
46
' !
46 13
35 *3
! 14
*
4!
46 35 1*
1' 1 6
*! 13 31
4 *! *3
33
35
11
15 35
4 *!
* *'
' 14
*
3!
33
13
*6 36
33 33
*
'
*6
4
11 4
41 36
*
44
*'
*1
1 ! *4
45 3 5
1 **
1 3*
*1
4*
4! 1*
* 33
3*
*
1*
44
41
1'
ersebaran data sample yang diujikan pada algoritma K)medoids 4)cluster dapat dilihat pada gambar !.*
(am&a) 8.' ersebaran data pada K)medoids 4)cluster
Data sampel pada lingkaran biru merupakan persebaran titik yang ada pada cluster 1, sedangkan persebaran data pada cluster * ditunjukkan dalam garis merah, dan untuk persebaran cluster 4 ada pada garis kuning.
8.3.1*e)+itu,a -a)a! Intracluster 3-cluster Cluster yang telah dipilih kemudian akan digunakan dalam perhitungan jarak intracluster antara masing)masing titik yang ada pada masing)masing cluster . 7ontohnya, =1 pada cluster 1 akan melakukan perhitungan intracluster sebanyak enam kali dengan titik)titik yang berada pada cluster tersebut. erhitungan jarak intracluster 3-cluster menggunakan perbandingan jarak 7anberra sebagai acuan dalam menentukan jarak dari masing)masing titik dalam cluster . $erikut merupakan tabel perhitungan intracluster 3-cluster yang ditunjukkan pada tabel !.'
%a&el 8. erhitungan jarak intracluster cluster 1
d@c1 :
=1
=*
3
44
4
*!
.**
d@c1 : d@c1 : d@c1 :
=1 =1 =1
=4 =3 =5
3 3 3
44 44 44
6 '
4' *6 46
.*6 .5 .4*
d@c1 :
=1
=6
3
44
!
13
.'3
d@c1 : d@c1 :
=1 =*
=' =4
3
44
* 6
4! 4'
.3 .3'
4
*!
d@c1 :
=*
=3
d@c1 : d@c1 : d@c1 :
=* =* =*
=5 =6 ='
4 4
*! *!
*6
.53
*! 4' 4'
' ! *
46 13 4!
.54 .' .45
4
*!
d@c1 : d@c1 :
=4 =4
=3 =5
4 6 6
'
*6 46
.4' .
d@c1 :
=4
=6
6
4'
!
13
.5
d@c1 :
=4
='
6
4'
*
4!
.51
d@c1 : d@c1 :
=3 =3
=5 =6
*6 *6
' !
46 13
.* .46
d@c1 :
=3
='
*6
*
4!
.!*
d@c1 : d@c1 : d@c1 :
=5 =5 =6
=6 =' ='
' ' !
46 46 13
! * *
13 4! 4!
.51 .5! 1.6
=abel !.' menunjukkan perhitungan titik untuk mencari jarak intracluster pada cluster 1 yang dilakukan dengan contoh sebagai berikut< dAc1 : (=1,=*"
: .** >etelah melakukan perhitungan intracluster untuk seluruh titik pada cluster 1, kemudian dilakukan pencarian untuk titik yang berada pada cluster * dan cluster 4 dengan cara yang sama seperti pada cluster 1. $erikut tabel yang menunjukkan perhitungan jarak intracluster menggunakan penerapan jarak 7anberra untuk cluster * seperti pada tabel !.!. %a&el 8.8 erhitungan jarak intracluster cluster *
d@c* :
=1
=*
36
1
41
31
.!
d@c* :
=4
36
1
=3 =5
36 36
1 1
* 11
.44
d@c* : d@c* :
36 33
d@c* : d@c* :
=6 ='
36 36
1 1
35 *3 46
! 14 1'
.' .1* .33 .4!
d@c* : d@c* :
=! =
36 36
1 1
35
1
1*
6
d@c* :
=1
36
1
d@c* : d@c* : d@c* :
=11 =1* =14
36 36 36
1 1 1
35 *
11 '
*'
14
d@c* : d@c* :
=13 =4
36
1
41
31
33 * 36
13 ' *
d@c* :
=3 =5
31 31
33 35
11 !
.'5
d@c* :
41 41
d@c* : d@c* :
=6 ='
41
31
*3
14
41 41
31 31
46 35
1' 1
.65 .3
41
31
1*
6
41
31
35
11
41 41
31 31
* *'
' 14
41
31
33
13
41 36
31 *
* 33
' 11
36 36 36
* * *
35 *3 46
! 14 1'
d@c* : d@c* : d@c* : d@c* :
=*
=! = =1 =11
.4* .!3 .6 .3 .4 .1 .3 .53 .!6
.55 1.1 .'6 .'3
d@c* : d@c* :
=1* =14
d@c* :
=13
d@c* : d@c* :
=3 =5
d@c* :
=6
d@c* :
='
d@c* : d@c* :
=! =
36
*
35
1
36
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36 36
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=4
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d@c* :
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=13 =6
d@c* : d@c* : d@c* :
=5
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35
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35
11
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1
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13
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=6
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d@c* : d@c* :
=1* =14
d@c* :
=13
d@c* : d@c* : d@c* :
=! = =1
d@c* : d@c* :
='
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d@c* :
=14
d@c* : d@c* :
=13 =
d@c* :
=1
d@c* : d@c* : d@c* :
d@c* : d@c* : d@c* :
=!
=
d@c* : d@c* : d@c* : d@c* :
=1
d@c* : d@c* : d@c* : d@c* : d@c* : d@c* :
=11
=1* =14
=11
=14 =13 =14 =13 =13
.16 .*! .3 .*! .*! .44 .3 .' .4
.4 .1' .! .44 .5* .*! .* .5* 1.1 .*' .6! .33 .16 .6! .!' .3 .'5 .' .3 .44
.53 . .*! .43 .53
=abel !.! menunjukkan perhitungan jarak intracluster pada titik)titik pada cluster *, yang menggunakan penerapan jarak 7anberra seperti pada perhitungan
cluster 1. >etelah perhitungan untuk cluster * selesai, dilanjutkan dengan perhitungan cluster 4 dengan penerapan jarak 7anberra yang akan ditunjukkan pada tabel !.
%a&el 8./ erhitungan jarak intercluster cluster 4
d@c4 :
=*
41
31
1
15
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d@c4 :
=4
41
31
1*
45
.5*
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=3 =5
41 41
31 31
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46 4
.*6 .*1
d@c4 :
=6
41
31
13
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41 41 41
31 31 31
31 15
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.3 .5 .4'
d@c4 :
=1
41
31
35
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41 41
31 31
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3! 33
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d@c4 :
=14
41
31
36
33
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41
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4
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d@c4 :
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d@c4 :
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1
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d@c4 : d@c4 : d@c4 :
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d@c4 : d@c4 :
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d@c4 :
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d@c4 :
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d@c4 :
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d@c4 : d@c4 :
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d@c4 :
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d@c4 :
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d@c4 :
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d@c4 : d@c4 :
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d@c4 : d@c4 : d@c4 :
= =1 =11
31 31 31
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d@c4 :
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31
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d@c4 :
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d@c4 : d@c4 :
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d@c4 :
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d@c4 : d@c4 :
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d@c4 :
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d@c4 : d@c4 : d@c4 :
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d@c4 : d@c4 :
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d@c4 : d@c4 : d@c4 :
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d@c4 : d@c4 :
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d@c4 :
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d@c4 : d@c4 : d@c4 :
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d@c4 :
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d@c4 : d@c4 : d@c4 :
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=abel !. menunjukkan hasil perhitungan jarak intracluster pada cluster 4 dengan penerapan jarak 7anberra. erhitungan tersebut sama dengan perhitungan yang digunakan pada cluster )cluster sebelumnya. >etelah perhitungan intracluster dari masing)masing cluster didapat, tahapan selanjutnya yaitu mencari nilai maksimum dari masing)masing cluster . Cilai maksimum dari masing)masing cluster ditunjukkan sebagai berikut< 1. Cluster 1
?a2 (dAc1" : 1.6 (=6,='" 2. Cluster *
?a2 (dAc*" : 1.1 (=*,=" 3. Cluster 4
?a2 (dAc4" : 1.1 (=14,=**", (=16,=**"
8.3.' *e)+itu,a -a)a! Intercluster 3#cluster
erhitungan
kemudian
dilanjutkan
dengan
pencarian
nilai
jarak
intercluster dengan membandingkan titik)titik pada salah satu cluster dengan titik) titik yang ada di cluster lainnya sampai habis. enerapan jarak 7anberra masih dilakukan dalam menentukkan nilai dari jarak intercluster , kemudian dilanjutkan dengan pencarian nilai minimum dari masing)masing erbandingan jarak intercluster yang ada dengan rumus seperti berikut<
erhitungan akan dimulai dengan perbandingan titik antara cluster 1 dan cluster *, kemudian diikuti dengan cluster )cluster lain hingga semua cluster telah dibandingkan. roses perhitungan jarak intercluster c1 dan c* dapat dilihat pada tabel !.1.
%a&el 8.10 erhitungan jarak intercluster c1 dan c*
d: d:
71 71
7* 7*
=1 =*
3 3
44 44
36
1
41
31
1.4' .!!
d:
71
7*
=4
3
44
36
*
1.
d: d:
71 71
7* 7*
=3 =5
3 3
44 44
33 35
11 !
1.44 1.35
d:
71
7*
=6
3
44
*3
14
1.15
d: d: d:
71 71 71
7* 7* 7*
=' =! =
3 3 3
44 44 44
46 35 1*
1' 1 6
1.1* 1.11 1.1
d:
71
7*
=1
3
44
71 71
7* 7*
=11 =1*
3 3
44 44
11 '
1.43
d: d:
35 * *'
14
1.31 1.1!
d: d: d:
71 71 71
7* 7* 7*
=14 =13 =1
3 3
44 44
4
*!
33 * 36
13 ' 1
1.*3 1.31 1.45
d:
71
7*
=*
4
*!
41
31
1.1
d: d:
71 71
7* 7*
=4 =3
4 4
*! *!
36 33
* 11
1.3 1.41
d:
71
7*
=5
4
*!
35
!
1.34
d:
71
7*
=6
71 71
7* 7*
=' =!
*! *! *!
*3 46 35
14 1' 1
1.13
d: d:
4 4 4
d:
71
7*
=
71 71
7* 7*
=1 =11
*! *!
1* 35
6 11
1.*5
d: d:
4 4 4
*!
*
'
d: d: d:
71 71 71
7* 7* 7*
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4
*!
*'
14
4 4
*! *!
d:
71
7*
=1
6
4'
33 * 36
13 ' 1
d:
71
7*
=*
d: d: d: d:
71 71 71 71
7* 7* 7* 7*
=4 =3 =5 =6
6 6
4' 4'
41 36
31 *
6 6 6
4' 4' 4'
33 35 *3
11 ! 14
=1
=*
=4
1. 1.' 1.41 1.31 1.1' 1.*1 1.31 1.43 .'4 1.' 1.4 1.31 1.!
d: d:
71 71
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6
4'
46
1'
6
4'
35
1
d:
71
7*
=
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6 6
4' 4'
1* 35
6 11
6
4'
*
'
d: d:
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=14 =13
6 6 6
4' 4' 4'
d:
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71
7*
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14 13 ' 1
d:
*' 33 * 36 41
31
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36
*
d:
71
7*
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33 35
11 !
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14
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46
1'
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71 71
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= =1
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35 1*
1 6
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35
11
d:
71
7*
=11
d: d:
71 71
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=1* =14
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* *'
' 14
d:
71
7*
=13
d:
71
7*
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'
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33 * 36
13 ' 1
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'
46
41
31
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46
36
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d:
71
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d: d:
71 71
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=5 =6
' '
46 46
33 35
11 !
'
46
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14
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71 71 71
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=' =! =
' '
46 46
46 35
1' 1
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46
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6
d:
71
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71
7*
=11
46 46
35 *
11 '
1.*6
d:
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d: d:
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=1* =14
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46 46
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14 13
1.6 1.1'
d:
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71 71
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* 36
' 1
1.*
d: d:
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13
41
31
d:
71
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d: d:
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! !
13 13
36 33
* 11
!
13
35
!
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71 71 71
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=6 =' =!
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13 13 13
*3 46 35
14 1' 1
.53 .'4 .!5
=3
=5
=6
1.! 1. 1.5 1.41 1.43 1.1* 1.*1 1.43
1.* .' .!1 .!* .'' 1.' 1.1 .!4 .6 1.1 1.4 .' 1.* 1.*6 1.4' 1.* 1.4 1.3 .! 1.*
.!' 1.! .!!
d: d:
71 71
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13
1*
6
!
13
35
11
d:
71
7*
=11
d: d: d:
71 71 71
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=1* =14 =13
! !
13 13
* *'
' 14
!
13
33
13
d: d:
71 71
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=1 =*
! * *
13 4! 4!
* 36
' 1
41
31
d:
71
7*
=4
71
7*
=3
4! 4!
36 33
* 11
1.*4
d:
* *
d: d:
71 71
7* 7*
=5 =6
*
4!
35
!
d:
71
7*
='
* *
4! 4!
*3 46
14 1'
1.5' 1.43
d: d: d:
71 71 71
7* 7* 7*
=! = =1
*
4!
35
1
*
4!
1*
6
d: d:
71 71
7* 7*
=11 =1*
* *
4! 4!
35 *
11 '
*
4!
*'
14
d:
71
7*
=14
d:
71
7*
=13
* *
4! 4!
33 *
13 '
='
.6 .!* . .5! .6 . 1.5 .* 1.36
1.*! 1.*5 1.33 1.3' 1.56 1.45 1.4' 1.56
=abel !.1 menunjukkan hasil perhitungan jarak antara titik yang berada pada cluster 1 dengan titik yang ada pada cluster *. erhitungan intercluster perlu memperhatikan baha semua titik pada salah satu cluster sudah dibandingkan dengan titik pada cluster lainnya. $erikut merupakan perhitungan untuk perbandingan cluster c1 dan c4 yang ditunjukkan pada tabel !.11.
%a&el 8.11 erhitungan jarak intercluster c1 dan c4
d: d:
71 71
d:
=1
74 74
=1 =*
3 3
44 44
41 1
31 15
.!! 1.4
71
74
=4
3
44
1*
45
.54
d:
71
74
=3
3
44
*1
46
.'*
d: d: d:
71 71 71
74 74 74
=5 =6 ='
3 3 3
44 44 44
*! 13 31
4 *! *3
.! .63 .!
d: d:
71 71
74 74
=! =
3 3
44 44
15
33 4
.54 .66
d:
71
74
=1
3
44
35
*!
.*
d: d: d:
71 71 71
74 74 74
=11 =1* =14
3 3 3
44 44 44
* *6 36
3! 33 33
.3 .!! .!
d: d:
71 71
74 74
=13 =15
3 3
44 44
*6 11
4 41
.!* .5
d:
71
74
=16
3
44
4
36
.!
d: d: d:
71 71 71
74 74 74
=1' =1! =1
3 3 3
44 44 44
* *' 1
44 *1 45
.'6 .6 .64
d: d:
71 71
74 74
=* =*1
3 3
44 44
! *4
3 5
.34 .1
d:
71
74
=**
3
44
1
1
1.53
d:
71
74
=*4
3
44
**
3*
.!1
d: d:
71 71
74 74
=*3 =*5
3 3
44 44
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4* *
.' 1.5
d:
71
74
=*6
3
44
1*
33
.63
d: d: d:
71 71 71
74 74 74
=*' =*! =*
3 3 3
44 44 44
3* 1* 41
* 44 1'
.! .5 1.
d: d:
71 71
74 74
=1 =*
4
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4
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41 1
31 15
1.1 1.4
d:
71
74
=4
45
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71 71
74 74
=3 =5
*! *!
1*
d: d:
4 4
.!! .!3
71
74
=6
13
*!
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d:
71
74
='
*! *! *!
46 4
d:
4 4 4
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.3
d: d:
71 71
74 74
=! =
4
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4
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15
33 4
.'* .!4
d:
71
74
=1
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71 71
74 74
=11 =1*
*! *!
35
d: d:
4 4 4
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* *6
3! 33
1.! 1.*
d: d: d:
71 71 71
74 74 74
=14 =13 =15
4 4
*! *!
4
*!
36 *6 11
33 4 41
1.1 .6 .6*
d:
71
74
=16
36
1.1
71
74
=1'
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4
d:
4 4
*
44
.!
d: d:
71 71
74 74
=1! =1
4 4
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.3 .61
d:
71
74
=*
3
.64
71 71
74 74
=*1 =**
*! *!
!
d: d:
4 4 4
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5 1
1.5 1.34
d:
71
74
=*4
3*
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71 71
74 74
=*3 =*5
*! *!
**
d: d:
4 4 4
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4* *
.!* 1.*
d: d: d:
71 71 71
74 74 74
=*6 =*' =*!
4 4 4
*! *! *!
1* 3* 1*
33 * 44
.!* .!! .6!
=*
d: d:
71 71
74 74
=* =1
4
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6
4'
d:
71
74
=*
d: d: d:
71 71 71
74 74 74
=4 =3 =5
6 6
4' 4'
6
4'
d: d:
71 71
74 74
=6 ='
6 6 6
4' 4' 4'
d:
71
74
=!
d:
71
74
=
6 6
4' 4'
d: d:
71 71
74 74
=1 =11
6
4'
d:
71
74
=1*
6 6
4' 4'
d: d: d:
71 71 71
74 74 74
=14 =13 =15
6
4'
6
4'
d: d:
71 71
74 74
=16 =1'
6 6
4' 4'
6
4'
d:
71
74
=1!
d: d:
71 71
74 74
=1 =*
6 6
4' 4'
d:
71
74
=*1
d:
71
74
=**
6 6 6
4' 4' 4'
d: d:
71 71
74 74
=*4 =*3
6
4'
6
4'
d:
71
74
=*5
d: d:
71 71
74 74
=*6 =*'
6 6
4' 4'
6
4'
d: d: d:
71 71 71
74 74 74
=*! =* =1
6 6
4' 4'
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d:
71
74
=*
d:
71
74
=4
d: d:
71 71
74 74
=3 =5
d:
71
74
=6
d: d:
71 71
74 74
=' =!
d:
71
74
=
d: d:
71 71
74 74
=1 =11
d: d: d:
71 71 71
74 74 74
=1* =14 =13
=4
=3
41 41
1' 31
1.' .'4
1
15
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1* *1 *!
45 46 4
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33
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=abel !.11 menunjukkan perbandingan antara titik)titik yang berada pada cluster 1 dengan titik)titik yang ada pada cluster 4 dengan penerapan jarak 7anberra dalam perhitungannya. $erikut perhitungan jarak intercluster yang dilakukan pada cluster * dengan cluster 4 yang dapat dilihat pada tabel !.1* %a&el 8.1' erhitungan jarak intercluster c* dan c4
d: d:
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d: d: d:
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d:
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d: d:
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d: d:
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d:
7*
74
=!
33
1.6
d: d: d:
7* 7* 7*
74 74 74
= =1 =11
35
1
35
1
35 35
1 1
15 35 *
4 *! 3!
.!3 .1 .65
d: d:
7* 7*
74 74
=1* =14
35
1
*6 36
33 33
.66 .31
d:
7*
74
=13
35 35
1 1
*6
4
.61
d: d:
7* 7*
74 74
=15 =16
35 35 35
1 1 1
11 4
41 36
.!5 .3
d:
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74
=1'
*
44
.3
d:
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=1!
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d: d:
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74 74
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35
1
35
1
1 !
45 3
1.*5 1.5
d:
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5
.''
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1 1
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35 35
d: d:
35
1
1 **
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d: d: d:
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74 74 74
=*3 =*5 =*6
35 35
1 1
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d:
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*
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d: d:
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35 1*
1 6
41 41
1' 31
.*3 1.1
d:
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15
.65
7* 7*
74 74
=4 =3
6 6
1
d: d:
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6
1* *1
45 46
.'1 .
d:
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74
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4
1.'
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74 74
=6 ='
6 6
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d: d:
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6
13 31
*! *3
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d: d: d:
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74 74 74
=! = =1
1* 1* 1*
6 6 6
15 35
33 4 *!
. .!3 1.*4
=!
=
d: d:
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74 74
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1*
6
* *6
3! 33
1.1 1.14
1*
6
d:
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74
=14
d: d: d:
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74 74 74
=13 =15 =16
1* 1*
6 6
36
33
1.45
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4 41 36
1.1 .'* 1.4
1*
6
d: d:
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6 6 6
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1.11 .3
d:
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d:
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6 6
1
45
1.55
!
3
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d: d:
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5 1
1.1 1.56
d:
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1.3
d: d: d:
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74 74 74
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6 6
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.6 1.6 .'6
d: d:
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6 11
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35 35 35
11 11 11
41 1
31 15
.'6 .56
d:
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45
1.1
d:
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46
.
d: d:
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35
11
35
11
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4 *!
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d:
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11 11
31
7* 7*
35 35
d: d:
35
11
15
33 4
1.*' 1.6
d: d: d:
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74 74 74
=1 =11 =1*
35 35
11 11
35
11
35 * *6
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.33 .!3 .!'
d:
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33
.61
7*
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11 11
36
d:
35 35
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4
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d: d:
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74 74
=15 =16
35 35
11 11
11 4
41 36
1.! .6
d:
7*
74
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44
.'*
7* 7*
74 74
=1! =1
11 11
*
d: d:
35 35 35
11
*' 1
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d:
7*
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3
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74 74
=*1 =**
11 11
!
d: d:
35 35 35
11
*4 1
5 1
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d: d: d:
7* 7* 7*
74 74 74
=*4 =*3 =*5
35 35 35
11 11 11
** *1 4!
3* 4* *
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=1
d: d:
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35
11
1* 3*
33 *
1.1! .3!
35
11
d:
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74 74 74
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35 35
11 11
1*
44
1.!
41 41 1
1' 31 15
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*
'
d: d:
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* * *
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45 46
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d:
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d:
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* *
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13
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d: d:
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d:
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15
4
1.1
d: d: d:
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74 74 74
=1 =11 =1*
*
'
*
'
* *
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d: d:
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36 *6
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d:
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11
41
1.!
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4 *
36 44
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d:
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d:
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1
45
1.6
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3 5
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1
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7* 7*
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d: d: d:
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74 74 74
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d: d:
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41 1
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14 14
1*
d: d:
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d:
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13
d: d:
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31
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d: d: d:
7* 7* 7*
74 74 74
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*' *' *'
14 14 14
15 35 *
4 *! 3!
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=11
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d: d:
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74 74
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14
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d: d: d:
7* 7* 7*
74 74 74
=15 =16 =1'
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14 14
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14
d: d:
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14 14 14
d:
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d: d:
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d: d: d:
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74 74 74
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14
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14
d: d:
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14 14
*'
14
d:
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74
=1
d: d:
7* 7*
74 74
=* =4
33 33
13 13
d:
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74
=3
d:
7*
74
=5
33 33 33
13 13 13
d: d:
7* 7*
74 74
=6 ='
33
13
33
13
d:
7*
74
=!
d: d:
7* 7*
74 74
= =1
33 33
13 13
33
13
d: d: d:
7* 7* 7*
74 74 74
=11 =1* =14
33 33
13 13
33
13
d:
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74
=13
d:
7*
74
=15
33 33
d: d:
7* 7*
74 74
=16 =1'
d:
7*
74
=1!
d: d:
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=1 =*
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=*1
d: d:
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d: d: d:
7* 7* 7*
74 74 74
=*3 =*5 =*6
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33 33
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4
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11 4 *
41 36 44
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33 33 33
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13
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13
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31 15 45
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d:
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74
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d:
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74
='
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13
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31
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=! =
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15
33 4
1.*5 1.1
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35
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d: d: d:
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74 74 74
=11 =1* =14
*
'
*
'
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3! 33 33
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d: d:
7* 7*
74 74
=13 =15
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4 41
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d:
7*
74
=16
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4
36
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d: d:
7* 7*
74 74
=1' =1!
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44 *1
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d:
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74
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1
45
1.6
d:
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3
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5 1
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d: d:
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d: d: d:
7* 7* 7*
74 74 74
=*6 =*' =*!
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1* 3* 1*
33 * 44
1.13 .' 1.6
d:
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74
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41
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=13
>etelah nilai perhitungan intercluster dari masing)masing perbandingan cluster didapatkan, selanjutnya melakukan pencarian nilai minimum dari masing) masing perbandingan tersebut, yang akan ditunjukkan sebagai berikut< 1. ?in d(c1,c*" : .53 *. ?in d(c1,c*" : .1* 4. ?in d(c*,c4" :
8.3.3 *e)+itu,a Ide!s Da"ies#$ouldi 3# cluster
erhitungan #ndeks dimulai dengan perhitungan yang akan dilanjutkan dengan perhitungan ma2 untuk cluster )cluster lain. $erikut merupakan hasil perhitungan tersebut. $erikut merupakan contoh perhitungan nilai ma2, yaitu< erbandingan nilai ma2 d(c1,c*" < d(c1,c4"
?a2 E(3.1' / *3.'5"F : *3.'5 $erdasarkan contoh perhitungan tersebut, dilakukan perhitungan nilai ma2 bagi setiap perbandingan cluster yang akan menghasilkan perhitungan seperti berikut. a. *e)+itu,a Ma!s d12' : d123
3.1' *3.'5
?a2 E(3.1' / *3.'5"F : *3.'5
&. *e)+itu,a Ma!s d12' : d'23
3.1' 4.1
?G E(3.1' / 4.1"F : 3.1'
. *e)+itu,a Ma!s d123 : d'23
*3.'5 4.1
?G E(*3.'5 / 4.1"F : *3.'5
>etelah melakukan perhitungan ma2 tersebut, perhitungan indeks Davis) $ouldin 4)cluster dilakukan dengan rumus sebagai berikut<
Cilai indeks Davies)$ouldin untuk 4)cluster yaitu 1'.!
8.4 Uji Validitas Ide!s Da"ies#$ouldi 4#cluster
engujian untuk perhitungan indeks Davies)$ouldin pada 3)cluster menggunakan data sampel yang sama dengan sebelumnya namun dikelompok menjadi 3 cluster seperti yang ditunjukkan pada tabel !.14
%a&el 8.13 Data sampel 3)cluster
Cluster 1
Cluster *
Cluster 4
Cluster 3
3 *1 4
44 46 *!
36 36 13
1 * *!
41 *! 31
31 4 *3
*1 1 1*
46 15 45
6
4'
33
11
35
*!
13
*!
35 46
! 1'
* *6
3! 33
*3
33 14
35
1
36
33
15
4
1* 35 *
6 11 '
*6 4 *
4 36 44
11 '
*6 41 46
*'
14
4!
*
*'
*1
33 *
13 '
3* 41
* 1'
! 1
13 45
!
3
*4 1
5 1
**
3*
*1 *
4* 4!
1*
33
1*
44
ersebaran data dari masing)masing cluster yang diujikan pada data sampel algoritma K)medoids dapat dilihat pada gambar !.4.
(am&a) 8.3 ersebaran data pada K)medoids 3)cluster
ersebaran data untuk cluster 1 digambarkan oleh titik)titik yang berada di dalam garis biru. ersebaran data cluster * digambarkan oleh titik)titik yang berada didalam garis merah. ersebaran data cluster 4 digambarkan oleh titik)titik yang berada pada garis ungu, sedangkan persebaran data sampel cluster 3 digambarkan pada titik)titik yang berada didalam garis kuning.
8.4.1 *e)+itu,a -a)a! Intracluster 4#cluster
Cluster yang telah dipilih kemudian digunakan dalam perhitungan jarak intracluster 3)cluster seperti
yang
dilakukan
pada
pengujian
4)cluster
sebelumnya. enerapan jarak 7anberra masih digunakan sebagai perhitungan jarak digunakan. $erikut merupakan perhitungan jarak intracluster 3)cluster yang ditunjukkan pada tabel)tabel berikut.
%a&el 8.14 erhitungan jarak intracluster cluster 1 pada pengujian 3)cluster
d@c1 : d@c1 : d@c1 : d@c1 : d@c1 : d@c1 :
=1
=* =4
=* =4 =3
3 3 3
44 44 44
*1 4 6
46 *! 4'
.'* .** .*6
=4
*1
46
4
*!
.!!
=3
*1
46
6
4'
.5'
=3
4
*!
6
4'
.3'
=abel !.13 menunjukkan perhitungan jarak intracluster pada cluster 1. erhitungan jarak intracluster akan menbandingkan seluruh titik yang ada dalam satu cluster .
%a&el 8.15 erhitungan jarak intracluster cluster * pada pengujian 3)cluster
d@c* :
=*
36
1
36
*
.44
d@c* :
=4
36
1
13
*!
1.1
d@c* :
=3
36
1
33
11
.'
d@c* :
=5
36
1
35
!
.1*
d@c* :
=6
36
1
46
1'
.4!
='
36
1
35
1
.4*
=! =
36 36
1 1
1* 35
6 11
.!3 .6
d@c* : d@c* :
=1 =11
36 36
1 1
* *'
' 14
.3 .4
d@c* :
=1*
36
1
33
13
.1
d@c* : d@c* :
=14 =4
36 36
1 *
* 13
' *!
.3 .'
d@c* :
=3
36
*
33
11
.41
d@c* : d@c* : d@c* :
=5 =6 ='
36 36 36
* * *
35 46 35
! 1' 1
.33 .* .3
=!
36
*
1*
6
1.1*
d@c* : d@c* :
= =1
36 36
* *
35 *
11 '
.4 .'1
d@c* : d@c* : d@c* :
=11 =1* =14
36 36 36
* * *
*' 33 *
14 13 '
.3' .* .'1
d@c* :
=3
13
*!
33
11
.5
d@c* : d@c* :
=5 =6
13 13
*! *!
35 46
! 1'
1.! .6!
d@c* :
='
13
*!
35
1
.'*
=!
13
*!
1*
6
.'*
= =1
13 13
*! *!
35 *
11 '
.6 .5
d@c* :
=11
13
*!
*'
14
.6!
d@c* : d@c* :
=1* =14
13 13
*! *!
33 *
13 '
.!5 .5
=5
33
11
35
!
.1'
=6 =' =!
33 33 33
11 11 11
46 35 1*
1' 1 6
.41 .*! .!'
d@c* : d@c* : d@c* :
d@c* :
d@c* : d@c* : d@c* :
d@c* : d@c* : d@c* : d@c* :
=1
=*
=4
=3
d@c* : d@c* :
= =1
33 33
11 11
35 *
11 '
.1 .34
d@c* :
=11
33
11
*'
14
.4*
d@c* :
=1*
33
11
33
13
.1*
d@c* : d@c* :
=14 =6
33 35
11 !
* 46
' 1'
.34 .3'
d@c* :
='
35
!
35
1
.31
d@c* : d@c* :
=! =
35 35
! !
1* 35
6 11
.'* .16
=1
35
!
*
'
.*!
d@c* :
=11
35
!
*'
14
.3
d@c* : d@c* :
=1* =14
35 35
! !
33 *
13 '
.*! .*!
d@c* :
='
46
1'
35
1
.1'
d@c* : d@c* :
=! =
46 46
1' 1'
1* 35
6 11
.! .44
=1 =11 =1*
46 46 46
1' 1' 1'
* *' 33
' 14 13
.5* .*! .*
d@c* :
=14
46
1'
*
'
.5*
d@c* :
=!
35
1
1*
6
1.1
d@c* : d@c* :
= =1
35 35
1 1
35 *
11 '
.*' .6!
=11
35
1
*'
14
.33
d@c* :
=1*
35
1
33
13
.16
d@c* : d@c* : d@c* :
=14 = =1
35 1* 1*
1 6 6
* 35 *
' 11 '
.6! .!' .3
=11 =1* =14
1* 1* 1*
6 6 6
*' 33 *
14 13 '
.'5 .' .3
=1 =11 =1*
35 35 35
11 11 11
* *' 33
' 14 13
.33 .44 .14
d@c* :
=14
35
11
*
'
.33
d@c* : d@c* : d@c* :
=1
=11 =1* =14
* * *
' ' '
*' 33 *
14 13 '
.43 .53 .
d@c* : d@c* :
=11
=1* =14
*' *'
14 14
33 *
13 '
.*! .43
d@c* :
=1*
=14
33
13
*
'
.53
d@c* :
d@c* : d@c* : d@c* :
d@c* :
d@c* : d@c* : d@c* : d@c* : d@c* : d@c* :
=5
=6
='
=!
=
%a&el 8.16 erhitungan jarak intracluster cluster 4 pada pengujian 3)cluster
d@c4 :
=*
41
31
*!
4
.*1
d@c4 : d@c4 :
=5 =6
35 35
*! *!
* *6
3! 33
.3! .3
d@c4 :
='
35
*!
36
33
.*4
d@c4 : d@c4 : d@c4 :
=! = =1
35 35 35
*! *! *!
*6 4 *
4 36 44
.34 .41 .4
d@c4 :
=11
35
*!
4!
*
.*5
d@c4 :
=1*
35
*!
3*
*
.5
d@c4 :
=14
35
*!
41
1'
.34
d@c4 :
=6
*
3!
*6
33
.1
d@c4 :
='
*
3!
36
33
.*'
d@c4 : d@c4 :
=! =
* *
3! 3!
*6 4
4 36
.16 .1'
=1
*
3!
*
44
.1
d@c4 : d@c4 :
=11 =1*
* *
3! 3!
4! 3*
* *
.55 .34
d@c4 : d@c4 : d@c4 :
=14 =' =!
* *6 *6
3! 33 33
41 36 *6
1' 33 4
.51 .*! .6
d@c4 :
=
*6
33
4
36
.**
=1
*6
33
*
44
.*
d@c4 : d@c4 :
=11 =1*
*6 *6
33 33
4! 3*
* *
.56 .33
d@c4 :
=14
*6
33
41
1'
.54
d@c4 : d@c4 :
=! =
36 36
33 33
*6 4
4 36
.43 .1
=1
36
33
*
44
.4'
=11
36
33
4!
*
.3'
d@c4 :
=1*
36
33
3*
*
.*5
d@c4 : d@c4 :
=14 =
36 *6
33 4
41 4
1' 36
.63 .*!
d@c4 : d@c4 : d@c4 :
=1 =11 =1*
*6 *6 *6
4 4 4
* 4! 3*
44 * *
.13 .51 .4!
d@c4 :
=14
*6
4
41
1'
.3!
d@c4 : d@c4 : d@c4 :
=1 =11 =1*
4 4 4
36 36 36
* 4! 3*
44 * *
.41 .31 .*6
=14 =11
4 *
36 44
41 4!
1' *
.5' .4!
=1*
*
44
3*
*
.*5
=14 =1* =14
* 4! 4!
44 * *
41 3* 41
1' * 1'
.45 .*4 .1!
d@c4 :
d@c4 :
d@c4 : d@c4 :
=3
=5
=6
='
=!
=
d@c4 : d@c4 : d@c4 : d@c4 : d@c4 : d@c4 :
=1
=11
d@c4 :
=1*
=14
3*
*
41
1'
.31
%a&el 8.1 erhitungan jarak intracluster cluster 3 pada pengujian 3)cluster
d@c3 :
=*
*1
46
1
15
.36
d@c3 : d@c3 :
=4 =3
*1 *1
46 46
1* 13
45 *!
.* .44
d@c3 :
=5
*1
46
33
.5
d@c3 :
=6
*1
46
*3
14
.53
d@c3 :
='
*1
46
15
4
.*1
d@c3 :
=!
*1
46
*6
.56
d@c3 : d@c3 :
= =1
*1 *1
46 46
11 '
41 46
.4 .5
=11
*1
46
*'
*1
.4
=1* =14 =13
*1 *1 *1
46 46 46
! 1 !
13 45 3
.! .* .5
d@c3 :
=15
*1
46
*4
5
.*1
d@c3 : d@c3 :
=16 =1'
*1 *1
46 46
1 **
1 3*
1.!6 .1
d@c3 :
=1!
*1
46
*1
4*
.6
d@c3 : d@c3 :
=1 =*
*1 *1
46 46
* 1*
4! 33
.!5 .4'
d@c3 : d@c3 : d@c3 :
=*1 =4 =3
*1 1 1
46 15 15
1* 1* 13
44 45 *!
.4* .64 .35
d@c3 :
=5
1
15
33
.!5
d@c3 :
=6
1
15
*3
14
.1
d@c3 : d@c3 :
=' =!
1 1
15 15
15
4 *6
.56 .64
d@c3 :
=
1
15
11
41
.61
d@c3 : d@c3 :
=1 =11
1 1
15 15
' *'
46 *1
.!' .43
d@c3 :
=1*
1
15
!
13
.33
d@c3 : d@c3 :
=14 =13
1 1
15 15
1 !
45 3
1.4 .!6
d@c3 :
=15
1
15
*4
5
.64
d@c3 :
=16
1
15
1
1
1.'!
d@c3 : d@c3 :
=1' =1!
1 1
15 15
** *1
3* 4*
.55 .31
d@c3 :
=1
1
15
*
4!
1.*3
d@c3 : d@c3 : d@c3 :
=* =*1 =3
1 1 1*
15 15 45
1* 1* 13
33 44 *!
.'* .6 .1
d@c3 : d@c3 : d@c3 : d@c3 :
=1
=*
=4
d@c3 :
=5
1*
45
33
.*6
d@c3 :
=6
1*
45
*3
14
.'
d@c3 :
='
1*
45
15
4
.1'
d@c3 : d@c3 : d@c3 :
=! = =1
1* 1* 1*
45 45 45
11 '
*6 41 46
.* .1 .*!
d@c3 : d@c3 :
=11 =1*
1* 1*
45 45
*' !
*1 13
.64 .64
d@c3 :
=14
1*
45
1
45
.!5
d@c3 : d@c3 : d@c3 :
=13 =15 =16
1* 1* 1*
45 45 45
! *4 1
3 5 1
.*' .3 1.'
d@c3 :
=1'
1*
45
**
3*
.4
d@c3 : d@c3 :
=1! =1
1* 1*
45 45
*1 *
4* 4!
.4* .'6
d@c3 :
=*
1*
45
1*
33
.11
d@c3 : d@c3 : d@c3 :
=*1 =5 =6
1* 13 13
45 *! *!
1* *3
44 33 14
.4 .33 .64
d@c3 :
='
13
*!
15
4
.*
d@c3 :
=!
13
*!
*6
.*5
d@c3 :
=
13
*!
11
41
.1'
d@c3 :
=1
13
*!
'
46
.36
d@c3 :
=11
13
*!
*'
*1
.36
d@c3 : d@c3 :
=1* =14
13 13
*! *!
! 1
13 45
.61 .!
d@c3 :
=13
13
*!
!
3
.35
d@c3 : d@c3 :
=15 =16
13 13
*! *!
*4 1
5 1
.54 1.!
d@c3 :
=1'
13
*!
**
3*
.3*
d@c3 :
=1!
13
*!
*1
4*
.*'
d@c3 : d@c3 :
=1 =*
13 13
*! *!
* 1*
4! 33
. .4
d@c3 : d@c3 : d@c3 :
=*1 =6 ='
13
*! 33 33
1* *3 15
44 14 4
.16 1. .41
d@c3 :
=!
33
*6
.*6
d@c3 : d@c3 : d@c3 :
= =1 =11
33 33 33
11 ' *'
41 46 *1
.*' .*4 .!5
d@c3 :
=1*
33
!
13
.5!
d@c3 : d@c3 :
=14 =13
33 33
1 !
45 3
.1 .11
d@c3 :
=15
33
*4
5
.5
=3
=5
d@c3 : d@c3 :
=16 =1'
33 33
1 **
1 3*
1.'6 .33
d@c3 :
=1!
33
*1
4*
.56
d@c3 : d@c3 : d@c3 :
=1 =* =*1
33 33 33
* 1* 1*
4! 33 44
.'1 .13 .*
d@c3 : d@c3 :
=' =!
*3 *3
14 14
15
4 *6
.'4 .'
d@c3 :
=
*3
14
11
41
.'!
d@c3 :
=1
*3
14
'
46
1.*
d@c3 : d@c3 :
=11 =1*
*3 *3
14 14
*' !
*1 13
.* .53
d@c3 :
=14
*3
14
1
45
1.4!
=13 =15 =16
*3 *3 *3
14 14 14
! *4 1
3 5 1
1.1 .61 1.'!
d@c3 : d@c3 :
=1' =1!
*3 *3
14 14
** *1
3* 4*
.5' .3
d@c3 :
=1
*3
14
*
4!
1.43
d@c3 : d@c3 :
=* =*1
*3 *3
14 14
1* 1*
33 44
.!! .''
d@c3 :
=!
15
4
*6
.35
d@c3 :
=
15
4
11
41
.*'
d@c3 : d@c3 :
=1 =11
15 15
4 4
' *'
46 *1
.3 .5
d@c3 :
=1*
15
4
!
13
.'!
d@c3 : d@c3 :
=14 =13
15 15
4 4
1 !
45 3
.4 .4*
=15 =16 =1'
15 15 15
4 4 4
*4 1 **
5 1 3*
.44 1.!4 .*4
d@c3 :
=1!
15
4
*1
4*
.*'
d@c3 :
=1
15
4
*
4!
.'!
d@c3 : d@c3 :
=* =*1
15 15
4 4
1* 1*
33 44
.1' .1
=
*6
11
41
.1
d@c3 : d@c3 :
=1 =11
*6 *6
' *'
46 *1
.* .61
d@c3 : d@c3 :
=1* =14
*6 *6
! 1
13 45
.46 .5
d@c3 : d@c3 : d@c3 :
=13 =15 =16
*6 *6 *6
! *4 1
3 5 1
.*' .'5 1.'4
d@c3 :
=1'
*6
**
3*
.65
d@c3 : d@c3 : d@c3 :
d@c3 : d@c3 : d@c3 :
d@c3 :
=6
='
=!
d@c3 : d@c3 :
=1! =1
*6 *6
*1 *
4* 4!
.5 .!*
d@c3 :
=*
*6
1*
33
.3
d@c3 : d@c3 : d@c3 :
=*1 =1 =11
11 11
*6 41 41
1* ' *'
44 46 *1
.*6 .4 .61
d@c3 : d@c3 :
=1* =14
11 11
41 41
! 1
13 45
.53 .!
d@c3 :
=13
11
41
!
3
.*!
=15
11
41
*4
5
.5
=16 =1'
11 11
41 41
1 **
1 3*
1.'' .3!
d@c3 :
=1!
11
41
*1
4*
.44
d@c3 : d@c3 : d@c3 :
=1 =* =*1
11 11 11
41 41 41
* 1* 1*
4! 33 44
.' .** .'
d@c3 : d@c3 :
=11 =1*
' '
46 46
*' !
*1 13
.!5 .51
d@c3 :
=14
'
46
1
45
.'6
d@c3 : d@c3 :
=13 =15
' '
46 46
! *4
3 5
.1* .'
=16
'
46
1
1
1.'
d@c3 :
=1'
'
46
**
3*
.5
d@c3 : d@c3 :
=1! =1
' '
46 46
*1 *
4* 4!
.56 .5!
d@c3 :
=*
'
46
1*
33
.46
d@c3 : d@c3 :
=*1 =1*
' *'
46 *1
1* !
44 13
.41 .'3
d@c3 : d@c3 : d@c3 :
=14 =13 =15
*' *' *'
*1 *1 *1
1 ! *4
45 3 5
1.1! .!5 .3
=16
*'
*1
1
1
1.!3
=1'
*'
*1
**
3*
.33
d@c3 : d@c3 :
=1! =1
*' *'
*1 *1
*1 *
4* 4!
.44 1.15
d@c3 :
=*
*'
*1
1*
33
.'3
d@c3 : d@c3 :
=*1 =14
*' !
*1 13
1* 1
44 45
.61 1.*1
d@c3 : d@c3 :
=13 =15
! !
13 13
! *4
3 5
.3! 1.5
d@c3 : d@c3 : d@c3 :
=16 =1' =1!
! ! !
13 13 13
1 ** *1
1 3* 4*
1.63 .' .!3
d@c3 :
=1
!
13
*
4!
1.6
d@c3 : d@c3 : d@c3 :
d@c3 :
d@c3 : d@c3 :
=
=1
=11
=1*
d@c3 : d@c3 :
=* =*1
! !
13 13
1* 1*
33 44
.'* .6
d@c3 :
=13
1
45
!
3
.!3
d@c3 : d@c3 : d@c3 :
=15 =16 =1'
1 1 1
45 45 45
*4 1 **
5 1 3*
1. .3 1.
=1! =1
1 1
45 45
*1 *
4* 4!
.5 .4'
d@c3 :
=*
1
45
1*
33
.6
d@c3 :
=*1
1
45
1*
44
.!!
d@c3 :
=15
!
3
*4
5
.5
d@c3 :
=16
!
3
1
1
1.'4
d@c3 :
=1'
!
3
**
3*
.3
=1!
!
3
*1
4*
.56
d@c3 : d@c3 :
=1 =*
! !
3 3
* 1*
4! 33
.64 .*5
d@c3 : d@c3 :
=*1 =16
! *4
3 5
1* 1
44 1
.4 1.!!
d@c3 :
=1'
*4
5
**
3*
.11
=1!
*4
5
*1
4*
.*6
=1
*4
5
*
4!
.!
d@c3 :
=*
*4
5
1*
33
.4!
d@c3 : d@c3 :
=*1 =1'
*4 1
5 1
1* **
44 3*
.5* 1.!'
d@c3 :
=1!
1
1
*1
4*
1.!5
=1 =* =*1
1 1 1
1 1 1
* 1* 1*
4! 33 44
1.*! 1.! 1.'
=1! =1 =*
** ** **
3* 3* 3*
*1 * 1*
4* 4! 33
.16 .!! .4*
=*1 =1 =*
** *1 *1
3* 4* 4*
1* * 1*
44 4! 33
.31 .1 .34
=*1
*1
4*
1*
44
.*
=* =*1 =*1
* * 1*
4! 4! 33
1* 1* 1*
33 44 44
.' .'! .13
d@c3 : d@c3 :
d@c3 :
d@c3 : d@c3 :
d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 :
=14
=13
=15
=16
=1'
=1!
d@c3 : d@c3 : d@c3 : d@c3 :
=1 =*
Cilai maksimum yang didapat dari perbandingan jarak intracluster dari pengujian 3)cluster yang sudah dilakukan adalah sebagai berikut< Cluster 1< nilai ma2 d@(c1" : .!! Cluster *< nilai ma2 d@(c*" : 1.1*
Cluster 4< nilai ma2 d@(c4" : .63 Cluster 3< nilai ma2 d@(c3" : 1.!!
8.4.' *e)+itu,a -a)a! Intercluster 4#cluster
>etelah melakukan perhitungan jarak intracluster , data sampel digunakan untuk melakukan perhitungan jarak intercluster antara titik dalam satu cluster dengan titik pada cluster lainnya. enerapan jarak 7anberra juga digunakan sebagai
acuan perhitungan
jarak
intercluster pada
pengujian 3)cluster .
erhitungan kemudian dilanjutkan dengan pencarian nilai min pada masing) masing perbandingan jarak intercluster dengan rumus sebagai berikut<
$erikut merupakan perhitungan jarak intercluster pengujian 3)cluster , yang ditunjukkan oleh tabel)tabel berikut. %a&el 8.18 erhitungan jarak intercluster cluster c1 dan c* pada pengujian 3)cluster
d:
71
7*
=1
3
44
36
1
1.4'
d: d:
71 71
7* 7*
=* =4
3 3
44 44
36 13
* *!
1. .63
d:
71
7*
=3
3
44
33
11
1.44
d: d:
71 71
7* 7*
=5 =6
3 3
44 44
35 46
! 1'
1.35 1.1*
d:
71
7*
='
3
44
35
1
1.11
d:
71
7*
=!
3
44
1*
6
1.1
d: d: d:
71 71 71
7* 7* 7*
= =1 =11
3 3 3
44 44 44
35 * *'
11 ' 14
1.43 1.31 1.1!
d: d:
71 71
7* 7*
=1* =14
3 3
44 44
33 *
13 '
1.*3 1.31
d:
71
7*
=1
*1
46
36
1
.3
d: d:
71 71
7* 7*
=* =4
*1 *1
46 46
36 13
* *!
.66 .44
d:
71
7*
=3
*1
46
33
11
.!
d: d: d:
71 71 71
7* 7* 7*
=5 =6 ='
*1 *1 *1
46 46 46
35 46 35
! 1' 1
1. .6* .6'
d:
71
7*
=!
*1
46
1*
6
.
d: d:
71 71
7* 7*
= =1
*1 *1
46 46
35 *
11 '
. .!4
d: d:
71 71
7* 7*
=11 =1*
*1 *1
46 46
*' 33
14 13
.5 .'
=1
=*
d: d:
71 71
7* 7*
=14 =1
*1 4
46 *!
* 36
' 1
.!4 1.45
d:
71
7*
=*
4
*!
36
*
1.3
d: d: d:
71 71 71
7* 7* 7*
=4 =3 =5
4 4 4
*! *! *!
13 33 35
*! 11 !
.65 1.41 1.34
d: d:
71 71
7* 7*
=6 ='
4 4
*! *!
46 35
1' 1
1. 1.'
d:
71
7*
=!
4
*!
1*
6
1.*5
d:
71
7*
=
4
*!
35
11
1.41
d: d:
71 71
7* 7*
=1 =11
4 4
*! *!
* *'
' 14
1.31 1.1'
d:
71
7*
=1*
4
*!
33
13
1.*1
d: d: d:
71 71 71
7* 7* 7*
=14 =1 =*
4 6 6
*! 4' 4'
* 36 36
' 1 *
1.31 1.43 1.'
d: d:
71 71
7* 7*
=4 =3
6 6
4' 4'
13 33
*! 11
.53 1.4
d:
71
7*
=5
6
4'
35
!
1.31
d: d:
71 71
7* 7*
=6 ='
6 6
4' 4'
46 35
1' 1
1.! 1.
d:
71
7*
=!
6
4'
1*
6
1.5
d:
71
7*
=
6
4'
35
11
1.41
d: d:
71 71
7* 7*
=1 =11
6 6
4' 4'
* *'
' 14
1.43 1.1*
d:
71
7*
=1*
6
4'
33
13
1.*1
d:
71
7*
=14
6
4'
*
'
1.43
=4
=3
%a&el 8.1/ erhitungan jarak intercluster cluster c1 dan c4 pada pengujian 3)cluster
d:
71
74
=1
3
44
41
31
.!!
d:
71
74
=*
3
44
*!
4
.!
d: d:
71 71
74 74
=4 =3
3 3
44 44
31 35
*3 *!
.! .*
d: d: d:
71 71 71
74 74 74
=5 =6 ='
3 3 3
44 44 44
* *6 36
3! 33 33
.3 .!! .!
d:
71
74
=!
3
44
*6
4
.!*
d: d: d:
71 71 71
74 74 74
= =1 =11
3 3 3
44 44 44
4 * 4!
36 44 *
.! .'6 1.5
d:
71
74
=1*
3
44
3*
*
.!
d: d: d:
71 71 71
74 74 74
=14 =1 =*
3 *1 *1
44 46 46
41 41 *!
1' 31 4
1. .*6 .*4
=1
=*
d: d:
71 71
74 74
=4 =3
*1 *1
46 46
31 35
*3 *!
.5* .3
d:
71
74
=5
*1
46
*
3!
.4
d: d: d:
71 71 71
74 74 74
=6 =' =!
*1 *1 *1
46 46 46
*6 36 *6
33 33 4
.*1 .3' .15
d: d:
71 71
74 74
= =1
*1 *1
46 46
4 *
36 44
.3* .*
d:
71
74
=11
*1
46
4!
*
.5'
d:
71
74
=1*
*1
46
3*
*
.33
d: d:
71 71
74 74
=14 =1
*1 4
46 *!
41 41
1' 31
.55 1.1
d:
71
74
=*
4
*!
*!
4
.!3
d: d: d:
71 71 71
74 74 74
=4 =3 =5
4 4 4
*! *! *!
31 35 *
*3 *! 3!
.3 .!! 1.!
d: d:
71 71
74 74
=6 ='
4 4
*! *!
*6 36
33 33
1.* 1.1
d:
71
74
=!
4
*!
*6
4
.6
d: d:
71 71
74 74
= =1
4 4
*! *!
4 *
36 44
1.1 .!
d:
71
74
=11
4
*!
4!
*
1.*
d:
71
74
=1*
4
*!
3*
*
.!!
d: d:
71 71
74 74
=14 =1
4 6
*! 4'
41 41
1' 31
1.' .'4
d:
71
74
=*
6
4'
*!
4
.'5
d: d:
71 71
74 74
=4 =3
6 6
4' 4'
31 35
*3 *!
.6 .
d: d: d:
71 71 71
74 74 74
=5 =6 ='
6 6 6
4' 4' 4'
* *6 36
3! 33 33
.' .'1 .!6
d:
71
74
=!
6
4'
*6
4
.65
d:
71
74
=
6
4'
4
36
.!3
d: d:
71 71
74 74
=1 =11
6 6
4' 4'
* 4!
44 *
.'1 1.4
d:
71
74
=1*
6
4'
3*
*
.!'
d:
71
74
=14
6
4'
41
1'
1.5
=4
=3
%a&el 8.'0 erhitungan jarak intercluster cluster c1 dan c3 pada pengujian 3)cluster
d: d:
71 71
=1
73 73
=1 =*
3 3
44 44
*1 1
46 15
.'* 1.4
d: d:
71 71
73 73
=4 =3
3 3
44 44
1* 13
45 *!
.54 .63
d:
71
73
=5
3
44
33
.54
d: d: d:
71 71 71
73 73 73
=6 =' =!
3 3 3
44 44 44
*3 15
14 4 *6
1.15 .66 .5
d: d:
71 71
73 73
= =1
3 3
44 44
11 '
41 46
.5 .4*
d:
71
73
=11
3
44
*'
*1
.6
d:
71
73
=1*
3
44
!
13
.'3
d: d:
71 71
73 73
=14 =13
3 3
44 44
1 !
45 3
.64 .34
d:
71
73
=15
3
44
*4
5
.1
d: d: d:
71 71 71
73 73 73
=16 =1' =1!
3 3 3
44 44 44
1 ** *1
1 3* 4*
1.53 .!1 .'
d: d:
71 71
73 73
=1 =*
3 3
44 44
* 1*
4! 33
.3 .63
d:
71
75
=*1
3
44
1*
44
.5
d: d:
71 71
73 73
=1 =*
*1 *1
46 46
*1 1
46 15
. .36
d:
71
73
=4
*1
46
1*
45
.*
d:
71
73
=3
*1
46
13
*!
.44
d: d:
71 71
73 73
=5 =6
*1 *1
46 46
*3
33 14
.5 .53
d:
71
73
='
*1
46
15
4
.*1
d: d:
71 71
73 73
=! =
*1 *1
46 46
11
*6 41
.56 .4
d: d: d:
71 71 71
73 73 73
=1 =11 =1*
*1 *1 *1
46 46 46
' *' !
46 *1 13
.5 .4 .!
d:
71
73
=14
*1
46
1
45
.*
d:
71
73
=13
*1
46
!
3
.5
d: d:
71 71
73 73
=15 =16
*1 *1
46 46
*4 1
5 1
.*1 1.!6
d:
71
73
=1'
*1
46
**
3*
.1
d: d:
71 71
73 73
=1! =1
*1 *1
46 46
*1 *
4* 4!
.6 .!5
d:
71
73
=*
*1
46
1*
33
.4'
d: d:
71 71
75 73
=*1 =1
*1 4
46 *!
1* *1
44 46
.4* .!!
d: d: d:
71 71 71
73 73 73
=* =4 =3
4 4 4
*! *! *!
1 1* 13
15 45 *!
1.4 .'1 .65
=*
=4
d: d:
71 71
73 73
=5 =6
4 4
*! *!
*3
33 14
.'* 1.13
d:
71
73
='
4
*!
15
4
.!4
d: d: d:
71 71 71
73 73 73
=! = =1
4 4 4
*! *! *!
11 '
*6 41 46
.53 .6* .54
d: d:
71 71
73 73
=11 =1*
4 4
*! *!
*' !
*1 13
.3 .'
d:
71
73
=14
4
*!
1
45
.61
d:
71
73
=13
4
*!
!
3
.64
d: d:
71 71
73 73
=15 =1 = 16
4 4
*! *!
*4 1
5 1
1.5 1.34
d:
71
73
=1'
4
*!
**
3*
.6
d: d: d:
71 71 71
73 73 73
=1! =1 =*
4 4 4
*! *! *!
*1 * 1*
4* 4! 33
.!* .45 .!*
d: d:
71 71
73 73
=*1 =1
4 6
*! 4'
1* *1
44 46
.6! .5'
d:
71
73
=*
6
4'
1
15
.3
d: d:
71 71
73 73
=4 =3
6 6
4' 4'
1* 13
45 *!
.46 .53
d:
71
73
=5
6
4'
33
.*
d:
71
73
=6
6
4'
*3
14
1.!
d: d:
71 71
73 73
=' =!
6 6
4' 4'
15
4 *6
.35 .4'
d:
71
73
=
6
4'
11
41
.4!
d: d:
71 71
73 73
=1 =11
6 6
4' 4'
' *'
46 *1
. .1
d: d: d:
71 71 71
73 73 73
=1* =14 =13
6 6 6
4' 4' 4'
! 1 !
13 45 3
.5 .'3 .1!
d:
71
73
=15
6
4'
*4
5
.'3
d:
71
73
=1 = 16
6
4'
1
1
1.66
d: d:
71 71
73 73
=1' =1!
6 6
4' 4'
** *1
3* 4*
.64 .64
d:
71
73
=1
6
4'
*
4!
.51
d: d:
71 71
73 73
=* =*1
6 6
4' 4'
1* 1*
33 44
.3* .4
=3
%a&el 8.'1 erhitungan jarak intercluster cluster c* c* dan c4 pada pengujian 3)cluster
d:
7*
d: d: d:
7* 7* 7*
=1
74
=1
36
1
41
31
.!
74 74 74
=* =4 =3
36 36 36
1 1 1
*! 31 35
4 *3 *!
.'3 .3' .3!
d: d:
7* 7*
74 74
=5 =6
36 36
1 1
* *6
3! 33
.!! .1
d:
7*
74
='
36
1
36
33
.64
d: d: d:
7* 7* 7*
74 74 74
=! = =1
36 36 36
1 1 1
*6 4 *
4 36 44
.!' .'4 .'6
d: d:
7* 7*
74 74
=11 =1*
36 36
1 1
4! 3*
* *
.34 .54
d:
7*
74
=14
36
1
41
1'
.35
d:
7*
74
=1
36
*
41
31
.53
d: d:
7* 7*
74 74
=* =4
36 36
* *
*! 31
4 *3
.33 .15
d:
7*
74
=3
36
*
35
*!
.1!
d: d: d:
7* 7* 7*
74 74 74
=5 =6 ='
36 36 36
* * *
* *6 36
3! 33 33
.63 .65 .4!
d: d:
7* 7*
74 74
=! =
36 36
* *
*6 4
4 36
.6 .3!
d:
7*
74
=1
36
*
*
44
.3'
d: d:
7* 7*
74 74
=11 =1*
36 36
* *
4! 3*
* *
.1 .*4
d:
7*
74
=14
36
*
41
1'
.*!
d:
7*
74
=1
13
*!
41
31
.5'
d: d:
7* 7*
74 74
=* =4
13 13
*! *!
*! 31
4 *3
.4' .5'
d:
7*
74
=3
13
*!
35
*!
.54
d: d:
7* 7*
74 74
=5 =6
13 13
*! *!
* *6
3! 33
.61 .5*
d: d: d:
7* 7* 7*
74 74 74
=' =! =
13 13 13
*! *! *!
36 *6 4
33 4 36
.'6 .36 .'1
d:
7*
74
=1
13
*!
*
44
.34
d:
7*
74
=11
13
*!
4!
*
.64
d: d:
7* 7*
74 74
=1* =14
13 13
*! *!
3* 41
* 1'
.5* .6*
d:
7*
74
=1
33
11
41
31
.'5
d: d:
7* 7*
74 74
=* =4
33 33
11 11
*! 31
4 *3
.6 .31
d:
7*
74
=3
33
11
35
*!
.35
d: d:
7* 7*
74 74
=5 =6
33 33
11 11
* *6
3! 33
.!4 .!6
d: d: d:
7* 7* 7*
74 74 74
=' =! =
33 33 33
11 11 11
36 *6 4
33 4 36
.6* .!* .6'
=*
=4
=3
d: d:
7* 7*
74 74
=1 =11
33 33
11 11
* 4!
44 *
.'1 .46
d:
7*
74
=1*
33
11
3*
*
.3'
d: d: d:
7* 7* 7*
74 74 74
=14 =1 =*
33 35 35
11 ! !
41 41 *!
1' 31 4
.4 .!6 .!1
d: d:
7* 7*
74 74
=4 =3
35 35
! !
31 35
*3 *!
.55 .56
d:
7*
74
=5
35
!
*
3!
.4
d:
7*
74
=6
35
!
*6
33
.6
d: d:
7* 7*
74 74
=' =!
35 35
! !
36 *6
33 4
.' .4
d:
7*
74
=
35
!
4
36
.'!
d: d: d:
7* 7* 7*
74 74 74
=1 =11 =1*
35 35 35
! ! !
* 4! 3*
44 * *
.!4 .51 .6
d: d:
7* 7*
74 74
=14 =1
35 46
! 1'
41 41
1' 31
.53 .3
d:
7*
74
=*
46
1'
*!
4
.3
d: d:
7* 7*
74 74
=4 =3
46 46
1' 1'
31 35
*3 *!
.*3 .46
d:
7*
74
=5
46
1'
*
3!
.5!
d:
7*
74
=6
46
1'
*6
33
.6
d: d:
7* 7*
74 74
=' =!
46 46
1' 1'
36 *6
33 4
.56 .55
d:
7*
74
=
46
1'
4
36
.5
d: d:
7* 7*
74 74
=1 =11
46 46
1' 1'
* 4!
44 *
.34 .11
d: d: d:
7* 7* 7*
74 74 74
=1* =14 =1
46 46 35
1' 1' 1
3* 41 41
* 1' 31
.43 .' .55
d:
7*
74
=*
35
1
*!
4
.36
d:
7*
74
=4
35
1
31
*3
.16
d: d:
7* 7*
74 74
=3 =5
35 35
1 1
35 *
*! 3!
.1 .65
d:
7*
74
=6
35
1
*6
33
.66
d: d:
7* 7*
74 74
=' =!
35 35
1 1
36 *6
33 4
.31 .61
d:
7*
74
=
35
1
4
36
.3
d: d:
7* 7*
74 74
=1 =11
35 35
1 1
* 4!
44 *
.3 .11
d: d: d:
7* 7* 7*
74 74 74
=1* =14 =1
35 35 1*
1 1 6
3* 41 41
* 1' 31
.*3 .*3 1.1
=5
=6
='
=!
d: d:
7* 7*
74 74
=* =4
1* 1*
6 6
*! 31
4 *3
1.' 1.15
d:
7*
74
=3
1*
6
35
*!
1.*4
d: d: d:
7* 7* 7*
74 74 74
=5 =6 ='
1* 1* 1*
6 6 6
* *6 36
3! 33 33
1.1 1.14 1.45
d: d:
7* 7*
74 74
=! =
1* 1*
6 6
*6 4
4 36
1.1 1.4
d:
7*
74
=1
1*
6
*
44
1.11
d:
7*
74
=11
1*
6
4!
*
1.6
d: d:
7* 7*
74 74
=1* =14
1* 1*
6 6
3* 41
* 1'
1.*1 .*
d:
7*
74
=1
35
11
41
31
.'6
d: d: d:
7* 7* 7*
74 74 74
=* =4 =3
35 35 35
11 11 11
*! 31 35
4 *3 *!
.' .3* .33
d: d:
7* 7*
74 74
=5 =6
35 35
11 11
* *6
3! 33
.!3 .!'
d:
7*
74
='
35
11
36
33
.61
d: d:
7* 7*
74 74
=! =
35 35
11 11
*6 4
4 36
.!4 .6
d:
7*
74
=1
35
11
*
44
.'*
d:
7*
74
=11
35
11
4!
*
.4'
d: d:
7* 7*
74 74
=1* =14
35 35
11 11
3* 41
* 1'
.3! .3
d:
7*
74
=1
*
'
41
31
.'3
d: d:
7* 7*
74 74
=* =4
* *
' '
*! 31
4 *3
.63 .'*
d: d: d:
7* 7* 7*
74 74 74
=3 =5 =6
* * *
' ' '
35 * *6
*! 3! 33
.!* .'5 .'!
d:
7*
74
='
*
'
36
33
.5
d:
7*
74
=!
*
'
*6
4
.'5
d: d:
7* 7*
74 74
= =1
* *
' '
4 *
36 44
.!! .65
d:
7*
74
=11
*
'
4!
*
.6*
d: d:
7* 7*
74 74
=1* =14
* *
' '
3* 41
* 1'
.' .35
d:
7*
74
=1
*'
14
41
31
.5
d: d:
7* 7*
74 74
=* =4
*' *'
14 14
*! 31
4 *3
.31 .5
d: d: d:
7* 7* 7*
74 74 74
=3 =5 =6
*' *' *'
14 14 14
35 * *6
*! 3! 33
.6* .61 .56
=
=1
=11
d: d:
7* 7*
74 74
=' =!
*' *'
14 14
36 *6
33 4
.! .5*
d:
7*
74
=
*'
14
4
36
.'3
d: d: d:
7* 7* 7*
74 74 74
=1 =11 =1*
*' *' *'
14 14 14
* 4! 3*
44 * *
.3' .4! .6
d: d:
7* 7*
74 74
=14 =1
*' 33
14 13
41 41
1' 31
.* .66
d:
7*
74
=*
33
13
*!
4
.5
d:
7*
74
=4
33
13
31
*3
.4
d: d:
7* 7*
74 74
=3 =5
33 33
13 13
35 *
*! 3!
.43 .'5
d:
7*
74
=6
33
13
*6
33
.''
d: d: d:
7* 7* 7*
74 74 74
=' =! =
33 33 33
13 13 13
36 *6 4
33 4 36
.53 .'4 .5
d: d:
7* 7*
74 74
=1 =11
33 33
13 13
* 4!
44 *
.61 .*5
d:
7*
74
=1*
33
13
3*
*
.4'
d: d:
7* 7*
74 74
=14 =1
33 *
13 '
41 41
1' 31
.*' .'3
d:
7*
74
=*
*
'
*!
4
.63
d:
7*
74
=4
*
'
31
*3
.'*
d: d:
7* 7*
74 74
=3 =5
* *
' '
35 *
*! 3!
.!* .'5
d:
7*
74
=6
*
'
*6
33
.'!
d: d:
7* 7*
74 74
=' =!
* *
' '
36 *6
33 4
.5 .'5
d: d: d:
7* 7* 7*
74 74 74
= =1 =11
* * *
' ' '
4 * 4!
36 44 *
.!! .65 .6*
d:
7*
74
=1*
*
'
3*
*
.'
d:
7*
74
=14
*
'
41
1'
.35
=1*
=14
%a&el 8.'' erhitungan jarak intercluster cluster c* dan c3 pada pengujian 3)cluster
d:
7*
d: d: d:
=1
73
=1
36
1
*1
46
.3
7* 7* 7*
73 73 73
=* =4 =3
36 36 36
1 1 1
1 1* 13
15 45 *!
.6* 1.13 1.1
d:
7*
73
=5
36
1
33
1.4
d: d:
7* 7*
73 73
=6 ='
36 36
1 1
*3 15
14 4
.33 1.1
d: d:
7* 7*
73 73
=! =
36 36
1 1
11
*6 41
1.1* 1.14
d:
7*
73
=1
36
1
'
46
1.4
d: d: d:
7* 7* 7*
73 73 73
=11 =1* =14
36 36 36
1 1 1
*' ! 1
*1 13 45
.6* .!' 1.51
d: d:
7* 7*
73 73
=13 =15
36 36
1 1
! *4
3 5
1.4 1.
d:
7*
73
=16
36
1
1
1
1.'!
d:
7*
73
=1'
36
1
**
3*
.'
d: d:
7* 7*
73 73
=1! =1
36 36
1 1
*1 *
4* 4!
. 1.5
d:
7*
73
=*
36
1
1*
33
1.**
d: d: d:
7* 7* 7*
73 73 73
=*1 =1 =*
36 36 36
1 * *
1* *1 1
44 46 15
1.1* .66 .56
d: d:
7* 7*
73 73
=4 =3
36 36
* *
1* 13
45 *!
.!6 .'
d:
7*
73
=5
36
*
33
1.5
d: d:
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35 35
*! *!
*4 1
5 1
.61 1.!
d:
74
73
=1'
35
*!
**
3*
.53
d: d: d:
74 74 74
73 73 73
=1! =1 =*
35 35 35
*! *! *!
*1 * 1*
4* 4! 33
.34 1.' .!
d:
74
73
=*1
35
*!
1*
44
.66
=4
=3
d: d:
74 74
73 73
=1 =*
* *
3! 3!
*1 1
46 15
.4 .'4
d:
74
73
=4
*
3!
1*
45
.5'
d: d: d:
74 74 74
73 73 73
=3 =5 =6
* * *
3! 3! 3!
13 *3
*! 33 14
.61 .5' .6'
d: d:
74 74
73 73
=' =!
* *
3! 3!
15
4 *6
.3* .!*
d:
74
73
=
*
3!
11
41
.6'
d:
74
73
=1
*
3!
'
46
.'5
d: d:
74 74
73 73
=11 =1*
* *
3! 3!
*' !
*1 13
.34 1.1*
d:
74
73
=14
*
3!
1
45
1.
d: d: d:
74 74 74
73 73 73
=13 =15 =16
* * *
3! 3! 3!
! *4 1
3 5 1
.66 .13 1.!
d: d:
74 74
73 73
=1' =1!
* *
3! 3!
** *1
3* 4*
.* .46
d:
74
73
=1
*
3!
*
4!
.
d: d:
74 74
73 73
=* =*1
* *
3! 3!
1* 1*
33 44
.36 .6
d:
74
73
=1
*6
33
*1
46
.*1
d:
74
73
=*
*6
33
1
15
.65
d: d:
74 74
73 73
=4 =3
*6 *6
33 33
1* 13
45 *!
.3! .5*
d:
74
73
=5
*6
33
33
.3
d: d:
74 74
73 73
=6 ='
*6 *6
33 33
*3 15
14 4
.5! .44
d: d: d:
74 74 74
73 73 73
=! = =1
*6 *6 *6
33 33 33
11 '
*6 41 46
.'3 .5! .6!
d: d:
74 74
73 73
=11 =1*
*6 *6
33 33
*' !
*1 13
.4' 1.5
d: d:
74 74
73 73
=14 =13
*6 *6
33 33
1 !
45 3
1.3 .5!
d:
74
73
=15
*6
33
*4
5
.14
d:
74
73
=16
*6
33
1
1
1.!!
d: d:
74 74
73 73
=1' =1!
*6 *6
33 33
** *1
3* 4*
.11 .*6
d:
74
73
=1
*6
33
*
4!
.4
d: d: d:
74 74 74
73 73 73
=* =*1 =1
*6 *6 36
33 33 33
1* 1* *1
33 44 46
.4' .51 .3'
d:
74
73
=*
36
33
1
15
.1
=5
=6
='
d: d:
74 74
73 73
=4 =3
36 36
33 33
1* 13
45 *!
.' .'6
d:
74
73
=5
36
33
33
.6'
d: d: d:
74 74 74
73 73 73
=6 =' =!
36 36 36
33 33 33
*3 15
14 4 *6
.!6 .5' .4
d: d:
74 74
73 73
= =1
36 36
33 33
11 '
41 46
.' .!3
d:
74
73
=11
36
33
*'
*1
.61
d:
74
73
=1*
36
33
!
13
1.**
d: d:
74 74
73 73
=14 =13
36 36
33 33
1 !
45 3
1.' .'5
d:
74
73
=15
36
33
*4
5
.3
d: d: d:
74 74 74
73 73 73
=16 =1' =1!
36 36 36
33 33 33
1 ** *1
1 3* 4*
1.1 .4! .54
d: d:
74 74
73 73
=1 =*
36 36
33 33
* 1*
4! 33
. .5
d: d:
74 74
73
=*1
36
33
1*
44
.'4
d:
74
73 73
=1 =*
*6 *6
4 4
*1 1
46 15
.15 .6
d:
74
73
=4
*6
4
1*
45
.3*
d:
74
73
=3
*6
4
13
*!
.36
d: d:
74 74
73 73
=5 =6
*6 *6
4 4
*3
33 14
.55 .53
d:
74
73
='
*6
4
15
4
.*'
d: d:
74 74
73 73
=! =
*6 *6
4 4
11
*6 41
.6 .5*
d: d: d:
74 74 74
73 73 73
=1 =11 =1*
*6 *6 *6
4 4 4
' *' !
46 *1 13
.6* .4* 1.
d: d:
74 74
73 73
=14 =13
*6 *6
4 4
1 !
45 3
.! .53
d: d:
74 74
73 73
=15 =16
*6 *6
4 4
*4 1
5 1
.1! 1.!!
d:
74
73
=1'
*6
4
**
3*
.1*
d:
74
73
=1!
*6
4
*1
4*
.*
d: d:
74 74
73 73
=1 =*
*6 *6
4 4
* 1*
4! 33
.!' .34
d:
74
73
=*1
*6
4
1*
44
.35
d: d: d:
74 74 74
73 73 73
=1 =* =4
4 4 4
36 36 36
*1 1 1*
46 15 45
.3* .!5 .6'
d:
74
73
=3
4
36
13
*!
.'1
=!
=
d: d:
74 74
73 73
=5 =6
4 4
36 36
*3
33 14
.65 .!
d:
74
73
='
4
36
15
4
.54
d: d: d:
74 74 74
73 73 73
=! = =1
4 4 4
36 36 36
11 '
*6 41 46
. .'5 .!*
d: d:
74 74
73 73
=11 =1*
4 4
36 36
*' !
*1 13
.55 1.1
d:
74
73
=14
4
36
1
45
1.
d:
74
73
=13
4
36
!
3
.'4
d: d:
74 74
73 73
=15 =16
4 4
36 36
*4 1
5 1
.4 1.1
d:
74
73
=1'
4
36
**
3*
.4*
d: d: d:
74 74 74
73 73 73
=1! =1 =*
4 4 4
36 36 36
*1 * 1*
4* 4! 33
.3! 1. .55
d: d:
74 74
73 73
=*1 =1
4 *
36 44
1* *1
44 46
.6 .*
d:
74
73
=*
*
44
1
15
.5!
d: d:
74 74
73 73
=4 =3
* *
44 44
1* 13
45 *!
.33 .34
d:
74
73
=5
*
44
33
.6'
d:
74
73
=6
*
44
*3
14
.54
d: d:
74 74
73 73
=' =!
* *
44 44
15
4 *6
.3 .63
d:
74
73
=
*
44
11
41
.3!
d: d:
74 74
73 73
=1 =11
* *
44 44
' *'
46 *1
.65 .*6
d: d: d:
74 74 74
73 73 73
=1* =14 =13
* * *
44 44 44
! 1 !
13 45 3
.' .6 .66
d: d:
74 74
73 73
=15 =16
* *
44 44
*4 1
5 1
.4* 1.!'
d: d:
74 74
73 73
=1' =1!
* *
44 44
** *1
3* 4*
.*6 .1!
d:
74
73
=1
*
44
*
4!
.3
d:
74
73
=*
*
44
1*
33
.56
d: d:
74 74
73 73
=*1 =1
* 4!
44 *
1* *1
44 46
.31 .5'
d:
74
73
=*
4!
*
1
15
.3!
d: d: d:
74 74 74
73 73 73
=4 =3 =5
4! 4! 4!
* * *
1* 13
45 *! 33
.' .64 .
d:
74
73
=6
4!
*
*3
14
.33
=1
=11
d: d:
74 74
73 73
=' =!
4! 4!
* *
15
4 *6
.'6 .'5
d:
74
73
=
4!
*
11
41
.''
d: d: d:
74 74 74
73 73 73
=1 =11 =1*
4! 4! 4!
* * *
' *' !
46 *1 13
.' .1 .!4
d: d:
74 74
73 73
=14 =13
4! 4!
* *
1 !
45 3
1.** .
d:
74
73
=15
4!
*
*4
5
.6'
d:
74
73
=16
4!
*
1
1
1.!5
d: d:
74 74
73 73
=1' =1!
4! 4!
* *
** *1
3* 4*
.6* .5*
d:
74
73
=1
4!
*
*
4!
1.*1
d: d: d:
74 74 74
73 73 73
=* =*1 =1
4! 4! 3*
* * *
1* 1* *1
33 44 46
. .'' .33
d: d:
74 74
73 73
=* =4
3* 3*
* *
1 1*
15 45
.' .65
d:
74
73
=3
3*
*
13
*!
.5*
d: d:
74 74
73 73
=5 =6
3* 3*
* *
*3
33 14
.!5 .65
d:
74
73
='
3*
*
15
4
.6*
d:
74
73
=!
3*
*
*6
.'
d: d:
74 74
73 73
= =1
3* 3*
* *
11 '
41 46
.6* .!*
d:
74
73
=11
3*
*
*'
*1
.4!
d: d:
74 74
73 73
=1* =14
3* 3*
* *
! 1
13 45
1.4 1.5
d: d: d:
74 74 74
73 73 73
=13 =15 =16
3* 3* 3*
* * *
! *4 1
3 5 1
.!3 .56 1.!
d: d:
74 74
73 73
=1' =1!
3* 3*
* *
** *1
3* 4*
.5 .4!
d: d:
74 74
73 73
=1 =*
3* 3*
* *
* 1*
4! 33
1.3 .'6
d:
74
73
=*1
3*
*
1*
44
.6*
d:
74
73
=1
41
1'
*1
46
.55
d: d:
74 74
73 73
=* =4
41 41
1' 1'
1 1*
15 45
.4 .'
d:
74
73
=3
41
1'
13
*!
.6*
d: d: d:
74 74 74
73 73 73
=5 =6 ='
41 41 41
1' 1' 1'
*3 15
33 14 4
. .*6 .'3
d:
74
73
=!
41
1'
*6
.'6
=1*
=14
d: d:
74 74
73 73
= =1
41 41
1' 1'
11 '
41 46
.'' .
d:
74
73
=11
41
1'
*'
*1
.1'
d: d: d:
74 74 74
73 73 73
=1* =14 =13
41 41 41
1' 1' 1'
! 1 !
13 45 3
.6 1.*! .
d: d:
74 74
73 73
=15 =16
41 41
1' 1'
*4 1
5 1
.63 1.!4
d:
74
73
=1'
41
1'
**
3*
.5
d:
74
73
=1!
41
1'
*1
4*
.5
d: d:
74 74
73 73
=1 =*
41 41
1' 1'
* 1*
4! 33
1.*6 .!!
d:
74
73
=*1
41
1'
1*
44
.'6
erhitungan kemudian dilanjutkan dengan pencarian nilai minimum dari masing)masing perbandingan jarak intercluster yang dapat dilihat sebagai berikut. Cilai min d(c1.c*" : .44 Cilai min d(c1.c4" : .15 Cilai min d(c1.c3" : Cilai min d(c*.c4" : .' Cilai min d(c*.c3" : Cilai min d(c4.c3" : .11 8.4.3 *e)+itu,a Ide!s Da"ies#$ouldi 4# cluster
erhitungan #ndeks Davies)$ouldin pada pengujian 3)cluster dimulai dengan pencarian nilai ma2 dengan rumus<
$erikut merupakan hasil pencarian ma2 pada masing)masing perbandingan
cluster yang ada pada pengujian data sampel 3)cluster .
a. *e)+itu,a Ma!s d12' : d123
6.6
1.14
?a2 E(6.6 / 1.14"F : 1.14
&. *e)+itu,a Ma!s d12' : d124
6.6 *.'6
?G E(6.6 / *.'6"F : 6.6
. *e)+itu,a Ma!s d12' : d'23
6.6 *5.13
?G E(6.6 / *5.13"F : *5.13
d. *e)+itu,a Ma!s d12' : d'24
6.6 4.
?G E(6.6 / 4."F : 6.6
e. *e)+itu,a Ma!s d12' : d324
6.6 **.1
?G E(6.6 / **.1"F : **.1
. *e)+itu,a Ma!s d123 : d124
1.14 *.'6
?G E(1.14 / *.'6"F : 1.14
,. *e)+itu,a Ma!s d123 : d'23
1.14 *5.13
?G E(1.14 / *5.13"F : *5.13
+. *e)+itu,a Ma!s d123 : d'24
1.14 4.
?G E(1.14 / 4."F : 1.14
i.
*e)+itu,a Ma!s d123 : d324
1.14 **.1
?G E(1.14 / **.1"F : **.1
j.
*e)+itu,a Ma!s d124 : d'23
*.'6
*5.13
?G E(*.'6 / *5,13"F : *5.13
!. *e)+itu,a Ma!s d124 : d'24
*.'6 4.
?G E(*.'6 / 4."F : 4.
l.
*e)+itu,a Ma!s d124 : d324
*.'6 **.1
?G E(*.'6 / **.1"F : **.1
m. *e)+itu,a Ma!s d'23 : d'24
*5.13 4.
?G E(*5.13 / 4."F : *5.13
. *e)+itu,a Ma!s d'23 : d324
*5.13 **.1
?G E(*5.13 / **.1"F : *5.31
o. *e)+itu,a Ma!s d'24 : d324
4. **.1
?G E(4. / **.1"F : **.1
erhitungan pencarian nilai ma2 dapat disederhanakan tampilannya dengan memasukkan hasil)hasil tersebut ke dalam tabel, yang ditunjukkan seperti pada tabel !.1. %a&el 8.'4 encarian nilai ma2 pada pengujian data sampel 3)cluster
d(c1,c4"
6.6
1.14
*e)&adi,a MA 1.14
d(c1,c3"
6.6
*.'6
6.6
d(c*,c4"
6.6
*5.13
*5.13
d(c*,c3"
6.6
4.
6.6
d(c4,c3" d(c1,c3"
6.6 1.14
**.1 *.'6
**.1 1.14
d(c*,c4"
1.14
*5.13
*5.13
d(c*,c3" d(c4,c3"
1.14 1.14
4. **.1
1.14 **.1
d(c*,c4"
*.'6
*5.13
*5.13
d(c*,c3" d(c4,c3"
*.'6 *.'6
4. **.1
4. **.1
d(c*,c3"
*5.13
4.
*5.13
d(c4,c3"
*5.13
**.1
*5.13
d(c4,c3"
4.
**.1
**.1
*e)+itu,a Ma!s
d(c1,c*"
d(c1,c4"
d(c1,c3"
d(c*,c4" d(c*,c3"
erhitungan kemudian dilanjutkan dengan pencarian nilai indeks Davies) $ouldin dengan rumus<
?aka perhitungan indeks Davies)$ouldin pada pengujian 3) cluster yaitu<
Dengan hasil dari indeks Davies)$ouldin yang didapat yaitu 65.'*
8.5 Uji Validitas Ide!s Da"ies#$ouldi 5#cluster
engujian validitas cluster menggunakan data sampel yang sama dengan membentuk 5 cluster pada hasil perhitungan algoritma K)medoids, yang dapat dilihat pada tabel !.*5 berikut.
%a&el 8.'5 Data sampel 5)cluster cluster 1
cluster '
cluster 3
cluster 4
cluster 5
1*
6
3
44
41
31
1
15
36
1
1
1
*
6
33
11
1*
45
36
*
6
4'
31
*3
*1
46
35
!
1
45
46
1'
*!
4
*3
14
*
4!
35
*!
4
*!
35
11
35
1
33
*
'
36
33
15
4
33
13
4
36
*
3!
*
'
*'
*1
*6
33
*'
14
*6
4!
*
*6
4
3*
*
11
41
41
1'
'
46
*
44
!
13
!
3
*4
5
**
3*
*1
4*
1*
33
1*
44
ersebaran data dari masing)masing cluster yang diujikan pada data sampel algoritma K)medoids 5)cluster dapat dilihat pada gambar !.3.
(am&a) 8.4 *e)se&a)a data samel 5#cluster
ersebaran data untuk cluster 1 1 digambarkan oleh titik)titik yang berada di dalam dalam garis garis merah. merah. ersebara ersebaran n data data cluster * * digambarkan oleh titik)titik yang berada didalam garis biru tua. ersebaran data cluster 4 4 digambarkan oleh titik) titik yang berada pada garis jingga, sedangkan persebaran data sampel cluster 3 digambarkan pada titik)titik yang berada didalam garis coklat serta persebaran data cluster 5 5 ditunjukkan dengan titik yang berada didalam garis biru muda. 8.5.1 8.5.1 *e)+itu, *e)+itu,a a -a)a! -a)a! Intracluster 5# 5#cluster
Cluster yang yang telah dipilih kemudian digunakan dalam perhitungan jarak intracluster 5) intracluster 5)cluster cluster seperti seperti yang dilakukan pada pengujian cluster sebelumnya. sebelumnya. enerap enerapan an jarak jarak 7anber 7anberra ra masih masih diguna digunakan kan sebaga sebagaii perhit perhitung ungan an jarak jarak dalam dalam menentukan menentukan hasil antara jarak satu titik dengan titik lainnya. lainnya. $erikut $erikut merupakan merupakan perhitungan jarak intracluster 5)cluster 5)cluster yang yang ditunjukkan pada tabel)tabel berikut. %a&el 8.'6 erhitungan jarak intracluster cluster intracluster cluster 1 1 pada pengujian 5)cluster
d@c1 :
=1
=*
1*
6
1
1
1.56
%a&el 8.' erhitungan jarak intracluster cluster intracluster cluster * * pada pengujian 5)cluster
d@c* : d@c* : d@c* :
=1
d@c* : d@c* : d@c* :
=*
=*
3
44
*
6
1.4
=4 =3
3 3
44 44
6 1
4' 45
.*6 .64
=5
3
44
*
4!
.3
=4 =3
* *
6 6
6 1
4' 45
1.** 1.3
d@c* : d@c* : d@c* : d@c* :
=4 =3
=5 =3
* 6
6 4'
* 1
4! 45
.'4 .'3
=5
6
4'
*
4!
.51
=5
1
45
*
4!
.4'
intracluster cluster 4 %a&el 8.'8 erhitungan jarak intracluster cluster 4 pada pengujian 5)cluster
d@c4 : d@c4 :
=* =4
41 41
31 31
33 31
11 *3
.'5 .3
d@c4 :
=3
41
31
46
1'
.3
d@c4 : d@c4 : d@c4 :
=5 =6 ='
41 41 41
31 31 31
35 35 36
*! 1 33
.4' .55 .*4
=!
41
31
4
36
.1'
d@c4 : d@c4 : d@c4 :
= =1 =11
41 41 41
31 31 31
*' *' 4!
*1 14 *
.4 .5 .35
d@c4 : d@c4 : d@c4 :
=1* =14 =4
41 41 33
31 31 11
3* 41 31
* 1' *3
.4* .31 .31
d@c4 : d@c4 :
=3 =5
33 33
11 11
46 35
1' *!
.41 .35
d@c4 :
=6
33
11
35
1
.*!
d@c4 :
='
33
11
36
33
.6*
=! =
33 33
11 11
4 *'
36 *1
.6' .55
d@c4 :
=1
33
11
*'
14
.4*
d@c4 : d@c4 :
=11 =1*
33 33
11 11
4! 3*
* *
.46 .3'
d@c4 : d@c4 : d@c4 :
=14 =3 =5
33 31 31
11 *3 *3
41 46 35
1' 1' *!
.4 .*3 .1*
d@c4 :
=6
31
*3
35
1
.16
d@c4 :
='
31
*3
36
33
.45
=! =
31 31
*3 *3
4 *'
36 *1
.43 .*'
d@c4 :
=1
31
*3
*'
14
.5
d@c4 : d@c4 :
=11 =1*
31 31
*3 *3
4! 3*
* *
.14 .11
d@c4 :
=14
31
*3
41
1'
.41
=5 =6
46 46
1' 1'
35 35
*! 1
.46 .1'
=' =! =
46 46 46
1' 1' 1'
36 4 *'
33 36 *1
.56 .5 .*5
d@c4 :
d@c4 : d@c4 :
d@c4 : d@c4 :
d@c4 : d@c4 : d@c4 : d@c4 : d@c4 :
=1
=*
=4
=3
d@c4 : d@c4 :
=1 =11
46 46
1' 1'
*' 4!
14 *
.*! .11
d@c4 :
=1*
46
1'
3*
*
.43
d@c4 : d@c4 : d@c4 :
=14 =6 ='
46 35 35
1' *! *!
41 35 36
1' 1 33
.' .1 .*4
d@c4 : d@c4 :
=! =
35 35
*! *!
4 *'
36 *1
.41 .4
=1
35
*!
*'
14
.6*
d@c4 :
=11
35
*!
4!
*
.*5
d@c4 : d@c4 :
=1* =14
35 35
*! *!
3* 41
* 1'
.5 .34
d@c4 :
='
35
1
36
33
.31
d@c4 : d@c4 : d@c4 :
=! = =1
35 35 35
1 1 1
4 *' *'
36 *1 14
.3 .4 .33
d@c4 : d@c4 :
=11 =1*
35 35
1 1
4! 3*
* *
.11 .*3
d@c4 :
=14
35
1
41
1'
.*3
d@c4 : d@c4 :
=! =
36 36
33 33
4 *'
36 *1
.1 .61
=1
36
33
*'
14
.!
=11
36
33
4!
*
.3'
d@c4 : d@c4 :
=1* =14
36 36
33 33
3* 41
* 1'
.*5 .63
d@c4 :
=
4
36
*'
*1
.55
d@c4 : d@c4 :
=1 =11
4 4
36 36
*' 4!
14 *
.'3 .31
=1* =14 =1
4 4 *'
36 36 *1
3* 41 *'
* 1' 14
.*6 .5' .*3
=11
*'
*1
4!
*
.1
=1*
*'
*1
3*
*
.4!
=14 =11
*' *'
*1 14
41 4!
1' *
.1' .4!
=1*
*'
14
3*
*
.6
=14 =1*
*' 4!
14 *
41 3*
1' *
.* .*4
=14
4!
*
41
1'
.1!
=14
3*
*
41
1'
.31
d@c4 :
d@c4 : d@c4 :
=5
=6
='
=!
d@c4 : d@c4 : d@c4 : d@c4 : d@c4 :
=
d@c4 : d@c4 : d@c4 : d@c4 : d@c4 : d@c4 : d@c4 :
=1
=11 =1*
%a&el 8.'/ erhitungan jarak intracluster cluster intracluster cluster 3 3 pada pengujian 5)cluster
d@c3 : d@c3 :
=* =4
1 1
15 15
1* *1
45 46
.64 .36
d@c3 :
=3
1
15
*!
4
.5*
d@c3 : d@c3 : d@c3 :
=5 =6 ='
1 1 1
15 15 15
4 15
*! 33 4
1.4 .!5 .56
d@c3 : d@c3 :
=! =
1 1
15 15
* *6
3! 33
.'4 .65
d@c3 :
=1
1
15
*6
.64
=11
1
15
*6
4
.6
=1* =14
1 1
15 15
11 '
41 46
.61 .!'
d@c3 :
=13
1
15
*
44
.5!
d@c3 : d@c3 : d@c3 :
=15 =16 =1'
1 1 1
15 15 15
! ! *4
13 3 5
.33 .!6 .64
d@c3 : d@c3 :
=1! =1
1 1
15 15
** *1
3* 4*
.55 .31
d@c3 :
=*
1
15
1*
33
.'*
d@c3 : d@c3 :
=*1 =4
1 1*
15 45
1* *1
44 46
.6 .*
d@c3 :
=3
1*
45
*!
4
.3!
d@c3 :
=5
1*
45
4
*!
.'1
d@c3 : d@c3 :
=6 ='
1* 1*
45 45
15
33 4
.*6 .1'
d@c3 :
=!
1*
45
*
3!
.5'
d@c3 : d@c3 :
= =1
1* 1*
45 45
*6
33 *6
.3! .*
d@c3 : d@c3 : d@c3 :
=11 =1* =14
1* 1* 1*
45 45 45
*6 11 '
4 41 46
.3* .1 .*!
d@c3 :
=13
1*
45
*
44
.33
d@c3 :
=15
1*
45
!
13
.64
d@c3 : d@c3 :
=16 =1'
1* 1*
45 45
! *4
3 5
.*' .3
d@c3 :
=1!
1*
45
**
3*
.4
d@c3 : d@c3 :
=1 =*
1* 1*
45 45
*1 1*
4* 33
.4* .11
d@c3 :
=*1
1*
45
1*
44
.4
=3 =5
*1 *1
46 46
*! 4
4 *!
.*4 .!!
=6 =' =!
*1 *1 *1
46 46 46
15 *
33 4 3!
.5 .*1 .4
d@c3 : d@c3 : d@c3 :
d@c3 : d@c3 : d@c3 : d@c3 : d@c3 :
=1
=*
=4
d@c3 : d@c3 :
= =1
*1 *1
46 46
*6
33 *6
.*1 .56
d@c3 :
=11
*1
46
*6
4
.15
d@c3 : d@c3 : d@c3 :
=1* =14 =13
*1 *1 *1
46 46 46
11 ' *
41 46 44
.4 .5 .*
d@c3 : d@c3 :
=15 =16
*1 *1
46 46
! !
13 3
.! .5
d@c3 :
=1'
*1
46
*4
5
.*1
d@c3 :
=1!
*1
46
**
3*
.1
d@c3 : d@c3 :
=1 =*
*1 *1
46 46
*1 1*
4* 33
.6 .4'
d@c3 :
=*1
*1
46
1*
44
.4*
d@c3 : d@c3 : d@c3 :
=5 =6 ='
*! *! *!
4 4 4
4 15
*! 33 4
.!3 .' .34
d@c3 : d@c3 :
=! =
*! *!
4 4
* *6
3! 33
.*5 .*4
d@c3 :
=1
*!
4
*6
.5!
d@c3 : d@c3 :
=11 =1*
*! *!
4 4
*6 11
4 41
.1' .35
=14
*!
4
'
46
.6
d@c3 :
=13
*!
4
*
44
.'
d@c3 : d@c3 :
=15 =16
*! *!
4 4
! !
13 3
.* .'
d@c3 :
=1'
*!
4
*4
5
.45
d@c3 : d@c3 :
=1! =1
*! *!
4 4
** *1
3* 4*
.* .1!
d@c3 : d@c3 : d@c3 :
=* =*1 =6
*! *! 4
4 4 *!
1* 1*
33 44 33
.5 .35 .'*
d@c3 :
='
4
*!
15
4
.!4
d@c3 :
=!
4
*!
*
3!
1.!
d@c3 : d@c3 :
= =1
4 4
*! *!
*6
33 *6
1.* .53
d@c3 :
=11
4
*!
*6
4
.6
d@c3 : d@c3 :
=1* =14
4 4
*! *!
11 '
41 46
.6* .54
d@c3 :
=13
4
*!
*
44
.!
d@c3 : d@c3 :
=15 =16
4 4
*! *!
! !
13 3
.' .64
d@c3 : d@c3 : d@c3 :
=1' =1! =1
4 4 4
*! *! *!
*4 ** *1
5 3* 4*
1.5 .6 .!*
d@c3 :
=3
=5
d@c3 : d@c3 :
=* =*1
4 4
*! *!
1* 1*
33 44
.!* .6!
d@c3 :
='
33
15
4
.41
d@c3 : d@c3 : d@c3 :
=! = =1
33 33 33
* *6
3! 33 *6
.5' .3 .*6
d@c3 : d@c3 :
=11 =1*
33 33
*6 11
4 41
.55 .*'
d@c3 :
=14
33
'
46
.*4
=13
33
*
44
.6'
d@c3 : d@c3 :
=15 =16
33 33
! !
13 3
.5! .11
d@c3 :
=1'
33
*4
5
.5
d@c3 : d@c3 : d@c3 :
=1! =1 =*
33 33 33
** *1 1*
3* 4* 33
.33 .56 .13
d@c3 : d@c3 :
=*1 =!
15
33 4
1* *
44 3!
.* .3*
d@c3 :
=
15
4
*6
33
.44
d@c3 : d@c3 :
=1 =11
15 15
4 4
*6
*6 4
.35 .*'
d@c3 :
=1*
15
4
11
41
.*'
d@c3 :
=14
15
4
'
46
.3
=13 =15
15 15
4 4
* !
44 13
.3 .'!
d@c3 :
=16
15
4
!
3
.4*
d@c3 : d@c3 :
=1' =1!
15 15
4 4
*4 **
5 3*
.44 .*4
d@c3 : d@c3 : d@c3 :
=1 =* =*1
15 15 15
4 4 4
*1 1* 1*
4* 33 44
.*' .1' .1
d@c3 :
=
*
3!
*6
33
.1
d@c3 :
=1
*
3!
*6
.!*
d@c3 : d@c3 :
=11 =1*
* *
3! 3!
*6 11
4 41
.16 .6'
d@c3 :
=14
*
3!
'
46
.'5
d@c3 : d@c3 :
=13 =15
* *
3! 3!
* !
44 13
.1 1.1*
d@c3 :
=16
*
3!
!
3
.66
d@c3 : d@c3 :
=1' =1!
* *
3! 3!
*4 **
5 3*
.13 .*
d@c3 : d@c3 :
=1 =*
* *
3! 3!
*1 1*
4* 33
.46 .36
d@c3 :
=*1
*
3!
1*
44
.6
d@c3 :
d@c3 : d@c3 :
=6
='
=!
d@c3 : d@c3 :
=1 =11
*6 *6
33 33
*6
*6 4
.'3 .6
d@c3 :
=1*
*6
33
11
41
.5!
d@c3 : d@c3 : d@c3 :
=14 =13 =15
*6 *6 *6
33 33 33
' * !
46 44 13
.6! .* 1.5
=16 =1'
*6 *6
33 33
! *4
3 5
.5! .14
d@c3 :
=1!
*6
33
**
3*
.11
d@c3 :
=1
*6
33
*1
4*
.*6
d@c3 : d@c3 :
=* =*1
*6 *6
33 33
1* 1*
33 44
.4' .51
d@c3 :
=11
*6
*6
4
.6
d@c3 : d@c3 : d@c3 :
=1* =14 =13
*6 *6 *6
11 ' *
41 46 44
.1 .* .63
d@c3 : d@c3 :
=15 =16
*6 *6
! !
13 3
.46 .*'
d@c3 :
=1'
*6
*4
5
.'5
d@c3 : d@c3 :
=1! =1
*6 *6
** *1
3* 4*
.65 .5
d@c3 :
=*
*6
1*
33
.3
d@c3 :
=*1
*6
1*
44
.*6
d@c3 : d@c3 :
=1* =14
*6 *6
4 4
11 '
41 46
.5* .6*
d@c3 :
=13
*6
4
*
44
.13
d@c3 : d@c3 :
=15 =16
*6 *6
4 4
! !
13 3
1. .53
=1' =1! =1
*6 *6 *6
4 4 4
*4 ** *1
5 3* 4*
.1! .1* .*
d@c3 :
=*
*6
4
1*
33
.34
d@c3 :
=*1
*6
4
1*
44
.35
d@c3 : d@c3 :
=14 =13
11 11
41 41
' *
46 44
.4 .3!
d@c3 :
=15
11
41
!
13
.53
d@c3 : d@c3 :
=16 =1'
11 11
41 41
! *4
3 5
.*! .5
d@c3 :
=1!
11
41
**
3*
.3!
d@c3 : d@c3 :
=1 =*
11 11
41 41
*1 1*
4* 33
.44 .**
d@c3 : d@c3 : d@c3 :
=*1 =13 =15
11 ' '
41 46 46
1* * !
44 44 13
.' .65 .51
d@c3 : d@c3 :
d@c3 : d@c3 : d@c3 :
=
=1
=11
=1*
=14
d@c3 : d@c3 :
=16 =1'
' '
46 46
! *4
3 5
.1* .'
d@c3 :
=1!
'
46
**
3*
.5
d@c3 : d@c3 : d@c3 :
=1 =* =*1
' ' '
46 46 46
*1 1* 1*
4* 33 44
.56 .46 .41
d@c3 : d@c3 :
=15 =16
* *
44 44
! !
13 3
.' .66
d@c3 :
=1'
*
44
*4
5
.4*
=1!
*
44
**
3*
.*6
d@c3 : d@c3 :
=1 =*
* *
44 44
*1 1*
4* 33
.1! .56
d@c3 :
=*1
*
44
1*
44
.31
d@c3 : d@c3 : d@c3 :
=16 =1' =1!
! ! !
13 13 13
! *4 **
3 5 3*
.3! 1.5 .'
=1 =*
! !
13 13
*1 1*
4* 33
.!3 .'*
d@c3 :
=*1
!
13
1*
44
.6
d@c3 : d@c3 :
=1' =1!
! !
3 3
*4 **
5 3*
.5 .3
=1
!
3
*1
4*
.56
d@c3 :
=*
!
3
1*
33
.*5
d@c3 : d@c3 :
=*1 =1!
! *4
3 5
1* **
44 3*
.4 .11
=1
*4
5
*1
4*
.*6
=* =*1
*4 *4
5 5
1* 1*
33 44
.4! .5*
=1 =* =*1
** ** **
3* 3* 3*
*1 1* 1*
4* 33 44
.16 .4* .31
=*
*1
4*
1*
33
.34
=*1
*1
4*
1*
44
.*
=*1
1*
33
1*
44
.13
d@c3 :
d@c3 : d@c3 :
d@c3 :
d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 : d@c3 :
=13
=15
=16
=1'
=1!
=1 =*
%a&el 8.30 erhitungan jarak intracluster cluster 5 pada pengujian 5)cluster
d@c5 : d@c5 : d@c5 : d@c5 : d@c5 :
=1
=* =4
36 36
1 1
36 35
* !
.44 .1*
=3 =5 =6
36 36 36
1 1 1
*3 35 *
14 11 '
.33 .6 .3
d@c5 : d@c5 :
=' =!
36 36
1 1
33 *
13 '
.1 .3
d@c5 :
=4
36
*
35
!
.33
d@c5 : d@c5 : d@c5 :
=3 =5 =6
36 36 36
* * *
*3 35 *
14 11 '
.54 .4 .'1
d@c5 : d@c5 :
=' =!
36 36
* *
33 *
13 '
.* .'1
d@c5 :
=3
35
!
*3
14
.53
d@c5 :
=5
35
!
35
11
.16
=6 ='
35 35
! !
* 33
' 13
.*! .*!
d@c5 :
=!
35
!
*
'
.*!
d@c5 : d@c5 : d@c5 :
=5 =6 ='
*3 *3 *3
14 14 14
35 * 33
11 ' 13
.4 .4 .44
=! =6
*3 35
14 11
* *
' '
.4 .33
='
35
11
33
13
.14
=! ='
35 *
11 '
* 33
' 13
.33 .53
=!
*
'
*
'
.
=!
33
13
*
'
.53
d@c5 : d@c5 :
=*
=4
=3
d@c5 : d@c5 : d@c5 : d@c5 : d@c5 : d@c5 : d@c5 :
=5
=6 ='
8asil perhitungan jarak intracluster yang didapatkan kemudian digunakan untuk pencarian nilai maksimum intracluster dari masing)masing cluster yang ada. $erikut merupakan nilai maksimum dari masing)masing cluster , yaitu< Cluster 1< nilai ma2 d@(c1" : 1.56 Cluster *< nilai ma2 d@(c*" : 1.** Cluster 4< nilai ma2 d@(c4" : .! Cluster 3< nilai ma2 d@(c3" : 1.1* Cluster 5< nilai ma2 d@(c5" : .'1 8.5.' *e)+itu,a -a)a! Intercluster 5#cluster
>etelah melakukan perhitungan jarak intracluster , data sampel digunakan untuk melakukan perhitungan jarak intercluster antara titik dalam satu cluster dengan titik pada cluster lainnya. enerapan jarak 7anberra juga digunakan sebagai
acuan perhitungan
jarak
intercluster pada
pengujian 5)cluster .
erhitungan kemudian dilanjutkan dengan pencarian nilai min pada masing) masing perbandingan jarak intercluster dengan rumus sebagai berikut<
$erikut merupakan perhitungan jarak intercluster pengujian 5)cluster , yang ditunjukkan oleh tabel)tabel berikut. %a&el 8.31 erhitungan jarak intercluster c1 dan c* pada pengujian 5)cluster
d:
71
7*
=1
d: d: d:
71 71 71
7* 7* 7*
=* =4 =3
d:
71
7*
=5
d: d: d:
71 71 71
7* 7* 7*
=1 =* =4
d: d:
71 71
7* 7*
=3 =5
=1
=*
1.1
1* 1*
6 6
3 *
44 6
1*
6
6
4'
1* 1* 1
6 6 1
1 * 3
45 4! 44
1
1
*
6
1 1
1 1
6 1
4' 45
1
1
*
4!
.3 1.*!
.'1 1.5 1.55 1.33 1.53 1.5 1.66
%a&el 8.3' erhitungan jarak intercluster c1 dan c4 pada pengujian 5)cluster
d:
71
74
=1
1*
6
41
31
1.1
d:
71
74
=*
1*
6
33
11
.!'
d: d:
71 71
74 74
=4 =3
1* 1*
6 6
31 46
*3 1'
1.15 .!
d:
71
74
=5
1*
6
35
*!
1.*4
d: d:
71 71
74 74
=6 ='
1* 1*
6 6
35 36
1 33
1.1 1.45
d:
71
74
=!
1*
6
4
36
1.4
d:
71
74
=
1*
6
*'
*1
.3
d: d:
71 71
74 74
=1 =11
1* 1*
6 6
*' 4!
14 *
.'5 1.6
d: d: d:
71 71 71
74 74 74
=1* =14 =1
1* 1* 1
6 6 1
3* 41 41
* 1' 31
1.*1 .* 1.!
d:
71
74
=*
1
1
33
11
1.'
d: d:
71 71
74 74
=4 =3
1 1
1 1
31 46
*3 1'
1.!' 1.!4
d:
71
74
=5
1
1
35
*!
1.!
d:
71
74
=6
1
1
35
1
1.!6
d: d:
71 71
74 74
=' =!
1 1
1 1
36 4
33 36
1.1 1.1
d: d: d:
71 71 71
74 74 74
= =1 =11
1 1 1
1 1 1
*' *' 4!
*1 14 *
1.!3 1.' 1.!5
d: d:
71 71
74 74
=1* =14
1 1
1 1
3* 41
* 1'
1.! 1.!4
=1
=*
%a&el 8.33 erhitungan jarak intercluster c1 dan c3 pada pengujian 5)cluster
d:
71
73
=1
1*
6
1
15
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d: d:
71 71
73 73
=* =4
1* 1*
6 6
71
73
=3
1*
6
45 46 4
.'1 .
d:
1* *1 *!
d:
71
73
=5
1*
6
71 71
73 73
=6 ='
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6 6
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d: d:
4 15
4
. .!3
d: d: d:
71 71 71
73 73 73
=! = =1
1* 1* 1*
6 6 6
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3! 33 *6
1.1 1.14 .''
d:
71
73
=11
1*
6
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4
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d: d: d:
71 71 71
73 73 73
=1* =14 =13
1* 1* 1*
6 6 6
11 ' *
41 46 44
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d:
71
73
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6
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73 73
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1* 1*
6 6
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d: d:
! ! *4
d: d: d:
71 71 71
73 73 73
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1* 1* 1*
6 6 6
** *1
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1*
33
1.3 .6 .'6
d: d: d:
71 71 71
73 73 73
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1* 1 1
6 1 1
1*
44
1 1*
15 45
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d:
71
73
=4
1
1
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46
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d:
71
73
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1
1
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73 73
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1 1
1 1
4 *!
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d: d:
*! 4
d:
71
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1
d: d:
71 71
73 73
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1 1
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33 4 3!
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71
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1
1
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d: d:
71 71
73 73
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1 1
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4 41
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d:
71
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1
1
'
46
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d:
71
73
=13
1
1
71 71
73 73
=15 =16
1 1
1 1
44 13
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d: d:
* ! !
3
d:
71
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1
1
d: d: d:
71 71 71
73 73 73
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1 1 1
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d:
71
73
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1
1
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44
1.'
=1
=*
1.'
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1.34 1.'6 1.!4
1.63 1.'4 1.!!
%a&el 8.34 erhitungan jarak intercluster c1 dan c5 pada pengujian 5)cluster
d:
71
75
=1
1*
6
36
1
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d:
71
75
=*
1*
6
36
*
1.1*
d:
71
75
=4
1*
6
35
!
.'*
d: d:
71 71
75 75
=3 =5
1* 1*
6 6
*3 35
14 11
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d: d: d:
71 71 71
75 75 75
=6 =' =!
1* 1* 1*
6 6 6
* 33 *
' 13 '
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d:
71
75
=1
1
1
36
1
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d: d: d:
71 71 71
75 75 75
=* =4 =3
1 1 1
1 1 1
36 35 *3
* ! 14
1.!6 1.'4 1.'!
d: d: d:
71 71 71
75 75 75
=5 =6 ='
1 1 1
1 1 1
35 * 33
11 ' 13
1.' 1.6! 1.!*
d:
71
75
=!
1
1
*
'
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=1
=*
%a&el 8.35 erhitungan jarak intercluster c* dan c4 pada pengujian 5)cluster
d:
7*
74
=1
3
44
41
31
.!!
d:
7*
74
=*
3
44
33
11
1.44
d:
7*
74
=4
3
44
31
*3
.!
d:
7*
74
=3
3
44
46
1'
1.1*
d:
7*
74
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3
44
35
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d: d:
7* 7*
74 74
=6 ='
3 3
44 44
35 36
1 33
1.11 .!
d:
7*
74
=!
3
44
4
36
.!
d:
7*
74
=
3
44
*'
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d: d:
7* 7*
74 74
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3 3
44 44
*' 4!
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d:
7*
74
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3
44
3*
*
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d: d: d:
7* 7* 7*
74 74 74
=14 =1 =*
3 * *
44 6 6
41 41 33
1' 31 11
1. 1.6* 1.*1
d: d:
7* 7*
74 74
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* *
6 6
31 46
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1.51 1.4'
d:
7*
74
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*
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35
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d: d:
7* 7*
74 74
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6 6
35 36
1 33
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d:
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d: d:
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74 74
= =1
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6 6
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=1
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d: d:
7* 7*
74 74
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* *
6 6
4! 3*
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1.33 1.5'
d:
7*
74
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*
6
41
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d: d: d:
7* 7* 7*
74 74 74
=1 =* =4
6 6 6
4' 4' 4'
41 33 31
31 11 *3
.'4 1.4 .6
d: d:
7* 7*
74 74
=3 =5
6 6
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46 35
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d:
7*
74
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6
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35
1
1.
d:
7*
74
='
6
4'
36
33
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d: d:
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74 74
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4 *'
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d:
7*
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6
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14
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d: d: d:
7* 7* 7*
74 74 74
=11 =1* =14
6 6 6
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d: d:
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74 74
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1 1
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41 33
31 11
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7*
74
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1
45
31
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d: d:
7* 7*
74 74
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1 1
45 45
46 35
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d:
7*
74
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1
45
35
1
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d:
7*
74
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1
45
36
33
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d: d:
7* 7*
74 74
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1 1
45 45
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d:
7*
74
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1
45
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14
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d: d:
7* 7*
74 74
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1 1
45 45
4! 3*
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d: d: d:
7* 7* 7*
74 74 74
=14 =1 =*
1 * *
45 4! 4!
41 41 33
1' 31 11
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d:
7*
74
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*
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31
*3
1.14
d:
7*
74
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*
4!
46
1'
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d: d:
7* 7*
74 74
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* *
4! 4!
35 35
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d:
7*
74
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*
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33
.
d: d:
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74 74
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d:
7*
74
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*
4!
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14
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d: d:
7* 7*
74 74
=11 =1*
* *
4! 4!
4! 3*
* *
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d:
7*
74
=14
*
4!
41
1'
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=4
=3
=5
%a&el 8.36 erhitungan jarak intercluster c* dan c3 pada pengujian 5)cluster
d:
7*
73
=1
3
44
1
15
1.4
d:
7*
73
=*
3
44
1*
45
.54
d:
7*
73
=4
3
44
*1
46
.'*
d:
7*
73
=3
3
44
*!
4
.!
d: d:
7* 7*
73 73
=5 =6
3 3
44 44
4
*! 33
.** .54
d:
7*
73
='
3
44
15
4
.66
d: d:
7* 7*
73 73
=! =
3 3
44 44
* *6
3! 33
.3 .!!
d:
7*
73
=1
3
44
*6
.5
=1
d: d:
7* 7*
73 73
=11 =1*
3 3
44 44
*6 11
4 41
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d:
7*
73
=14
3
44
'
46
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d: d: d:
7* 7* 7*
73 73 73
=13 =15 =16
3 3 3
44 44 44
* ! !
44 13 3
.'6 .'3 .34
d: d:
7* 7*
73 73
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3 3
44 44
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5 3*
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d:
7*
73
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3
44
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4*
.'
d:
7*
73
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3
44
1*
33
.63
d: d:
7* 7*
73 73
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3 *
44 6
1* 1
44 15
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d:
7*
73
=*
*
6
1*
45
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d: d: d:
7* 7* 7*
73 73 73
=4 =3 =5
* * *
6 6 6
*1 *! 4
46 4 *!
1.53 1.54 .!5
d: d:
7* 7*
73 73
=6 ='
* *
6 6
15
33 4
1.3 1.5
d:
7*
73
=!
*
6
*
3!
1.65
d: d:
7* 7*
73 73
= =1
* *
6 6
*6
33 *6
1.6* 1.*6
d:
7*
73
=11
*
6
*6
4
1.5
d:
7*
73
=1*
*
6
11
41
1.4'
d: d:
7* 7*
73 73
=14 =13
* *
6 6
' *
46 44
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d:
7*
73
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*
6
!
13
1.
d: d:
7* 7*
73 73
=16 =1'
* *
6 6
! *4
3 5
1.43 1.64
d: d: d:
7* 7* 7*
73 73 73
=1! =1 =*
* * *
6 6 6
** *1 1*
3* 4* 33
1.5! 1.51 1.3'
d:
7*
73
=*1
*
6
1*
44
1.31
d:
7*
73
=1
6
4'
1
15
.3
d: d:
7* 7*
73 73
=* =4
6 6
4' 4'
1* *1
45 46
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d:
7*
73
=3
6
4'
*!
4
.'5
d: d:
7* 7*
73 73
=5 =6
6 6
4' 4'
4
*! 33
.3' .*
d:
7*
73
='
6
4'
15
4
.35
d: d:
7* 7*
73 73
=! =
6 6
4' 4'
* *6
3! 33
.' .'1
d: d: d:
7* 7* 7*
73 73 73
=1 =11 =1*
6 6 6
4' 4' 4'
*6 11
*6 4 41
.4' .65 .4!
=*
=4
d: d:
7* 7*
73 73
=14 =13
6 6
4' 4'
' *
46 44
. .'1
d:
7*
73
=15
6
4'
!
13
.5
d: d: d:
7* 7* 7*
73 73 73
=16 =1' =1!
6 6 6
4' 4' 4'
! *4 **
3 5 3*
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d: d:
7* 7*
73 73
=1 =*
6 6
4' 4'
*1 1*
4* 33
.64 .3*
d:
7*
73
=*1
6
4'
1*
44
.4
d:
7*
73
=1
1
45
1
15
1.4
d: d:
7* 7*
73 73
=* =4
1 1
45 45
1* *1
45 46
.!5 .*
d:
7*
73
=3
1
45
*!
4
1.1
d: d: d:
7* 7* 7*
73 73 73
=5 =6 ='
1 1 1
45 45 45
4 15
*! 33 4
.61 .1 .4
d: d:
7* 7*
73 73
=! =
1 1
45 45
* *6
3! 33
1. 1.3
d:
7*
73
=1
1
45
*6
.5
d: d:
7* 7*
73 73
=11 =1*
1 1
45 45
*6 11
4 41
.! .!
d:
7*
73
=14
1
45
'
46
.'6
d:
7*
73
=13
1
45
*
44
.6
d: d:
7* 7*
73 73
=15 =16
1 1
45 45
! !
13 3
1.*1 .!3
d:
7*
73
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1
45
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5
1.
d: d:
7* 7*
73 73
=1! =1
1 1
45 45
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3* 4*
1. .5
d: d: d:
7* 7* 7*
73 73 73
=* =*1 =1
1 1 *
45 45 4!
1* 1* 1
33 44 15
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d:
7*
73
=*
*
4!
1*
45
.'6
d:
7*
73
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*
4!
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46
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d: d:
7* 7*
73 73
=3 =5
* *
4! 4!
*! 4
4 *!
.! .45
d:
7*
73
=6
*
4!
33
.'1
d: d:
7* 7*
73 73
=' =!
* *
4! 4!
15 *
4 3!
.'! .
d:
7*
73
=
*
4!
*6
33
.4
d: d:
7* 7*
73 73
=1 =11
* *
4! 4!
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*6 4
.!* .!'
d: d: d:
7* 7* 7*
73 73 73
=1* =14 =13
* * *
4! 4! 4!
11 ' *
41 46 44
.' .5! .3
=3
=5
d: d:
7* 7*
73 73
=15 =16
* *
4! 4!
! !
13 3
1.6 .64
d:
7*
73
=1'
*
4!
*4
5
.!
d: d: d:
7* 7* 7*
73 73 73
=1! =1 =*
* * *
4! 4! 4!
** *1 1*
3* 4* 33
.!! .1 .'
d:
7*
73
=*1
*
4!
1*
44
.'!
%a&el 8.3 erhitungan jarak intercluster c* dan c5 pada pengujian 5)cluster
d:
7*
75
=1
3
44
36
1
1.4'
d:
7*
75
=*
3
44
36
*
1.
d:
7*
75
=4
3
44
35
!
1.35
d: d:
7* 7*
75 75
=3 =5
3 3
44 44
*3 35
14 11
1.15 1.43
d:
7*
75
=6
3
44
*
'
1.31
d: d:
7* 7*
75 75
=' =!
3 3
44 44
33 *
13 '
1.*3 1.31
d:
7*
75
=1
*
6
36
1
1.1'
d:
7*
75
=*
*
6
36
*
1.36
d: d:
7* 7*
75 75
=4 =3
* *
6 6
35 *3
! 14
1.6 1.*1
d: d: d:
7* 7* 7*
75 75 75
=5 =6 ='
* * *
6 6 6
35 * 33
11 ' 13
1.*1 .5 1.41
d:
7*
75
=!
*
6
*
'
.5
d: d:
7* 7*
75 75
=1 =*
6 6
4' 4'
36 36
1 *
1.43 1.'
d:
7*
75
=4
6
4'
35
!
1.31
d:
7*
75
=3
6
4'
*3
14
1.!
d: d:
7* 7*
75 75
=5 =6
6 6
4' 4'
35 *
11 '
1.41 1.43
d: d: d:
7* 7* 7*
75 75 75
=' =! =1
6 6 1
4' 4' 45
33 * 36
13 ' 1
1.*1 1.43 1.51
d: d: d:
7* 7* 7*
75 75 75
=* =4 =3
1 1 1
45 45 45
36 35 *3
* ! 14
1.*4 1.5! 1.4!
d:
7*
75
=5
1
45
35
11
1.3!
d:
7*
75
=6
1
45
*
'
1.6
d: d:
7* 7*
75 75
=' =!
1 1
45 45
33 *
13 '
1.4! 1.6
d:
7*
75
=1
*
4!
36
1
1.5
d: d:
7* 7*
75 75
=* =4
* *
4! 4!
36 35
* !
1.*4 1.5'
=1
=*
=4
=3
=5
d: d:
7* 7*
75 75
=3 =5
* *
4! 4!
*3 35
14 11
1.43 1.3'
d:
7*
75
=6
*
4!
*
'
1.56
d: d:
7* 7*
75 75
=' =!
* *
4! 4!
33 *
13 '
1.4' 1.56
%a&el 8.38 erhitungan jarak intercluster c4 dan c3 pada pengujian 5)cluster
d:
74
73
=1
41
31
1
15
.'
d:
74
73
=*
41
31
1*
45
.5*
d:
74
73
=4
41
31
*1
46
.*6
d:
74
73
=3
41
31
*!
4
.*1
d:
74
73
=5
41
31
4
*!
1.1
d: d:
74 74
73 73
=6 ='
41 41
31 31
15
33 4
.5 .4'
d:
74
73
=!
41
31
*
3!
.11
d: d:
74 74
73 73
= =1
41 41
31 31
*6
33 *6
.1* .''
d:
74
73
=11
41
31
*6
4
.11
d:
74
73
=1*
41
31
11
41
.6*
d: d:
74 74
73 73
=14 =13
41 41
31 31
' *
46 44
.' .13
d: d: d:
74 74 74
73 73 73
=15 =16 =1'
41 41 41
31 31 31
! ! *4
13 3 5
1.! .6 .*5
d:
74
73
=1!
41
31
**
3*
.1!
d: d:
74 74
73 73
=1 =*
41 41
31 31
*1 1*
4* 33
.4* .3!
d:
74
73
=*1
41
31
1*
44
.55
d:
74
73
=1
33
11
1
15
.55
d: d:
74 74
73 73
=* =4
33 33
11 11
1* *1
45 46
1. .!
d: d: d:
74 74 74
73 73 73
=3 =5 =6
33 33 33
11 11 11
*! 4
4 *! 33
.6 1.41 1.*6
d: d: d:
74 74 74
73 73 73
=' =! =
33 33 33
11 11 11
15 * *6
4 3! 33
1.5 .!4 .!6
d:
74
73
=1
33
11
*6
1.'
d:
74
73
=11
33
11
*6
4
.!*
d: d:
74 74
73 73
=1* =14
33 33
11 11
11 '
41 46
1.! 1.*6
d:
74
73
=13
33
11
*
44
.'1
d: d:
74 74
73 73
=15 =16
33 33
11 11
! !
13 3
.!1 1.*6
=1
=*
d: d:
74 74
73 73
=1' =1!
33 33
11 11
*4 **
5 3*
.5 .*
d:
74
73
=1
33
11
*1
4*
.!3
d: d: d:
74 74 74
73 73 73
=* =*1 =1
33 33 31
11 11 *3
1* 1* 1
33 44 15
1.1' 1.' .6
d: d:
74 74
73 73
=* =4
31 31
*3 *3
1* *1
45 46
.'4 .5*
d:
74
73
=3
31
*3
*!
4
.4
d:
74
73
=5
31
*3
4
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74 74
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d: d:
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d: d:
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d:
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74 74
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74 74 74
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1
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1
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d: d:
74 74
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74 74 74
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74 74
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74 74 74
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74 74
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74
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41
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74 74
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d: d: d:
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74
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74
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74 74 74
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='
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d: d:
74 74
73 73
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74
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d: d:
74 74
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74
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74
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d: d: d:
74 74 74
73 73 73
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d: d:
74 74
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74
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74 74
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74
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74
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74 74
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74
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33
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d: d:
74 74
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15 *
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d: d: d:
74 74 74
73 73 73
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d:
74
73
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14
11
41
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74
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46
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d: d:
74 74
73 73
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74
73
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74 74
73 73
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74
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74 74
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74 74 74
73 73 73
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d: d:
74 74
73 73
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4 *!
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d:
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d: d: d:
74 74 74
73 73 73
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d: d:
74 74
73 73
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d:
74
73
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*
11
41
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d:
74
73
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46
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74 74
73 73
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44 13
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d:
74
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3
.
d: d: d:
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d: d:
74 74
73 73
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74
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1
15
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d: d:
74 74
73 73
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45 46
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d:
74
73
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4
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d:
74
73
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4
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d: d:
74 74
73 73
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15
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74
73
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74 74
73 73
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d: d: d:
74 74 74
73 73 73
=11 =1* =14
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4 41 46
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d:
74
73
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44
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74
73
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13
1.4
d: d:
74 74
73 73
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74
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d: d:
74 74
73 73
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74
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d: d:
74 74
73 73
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41 41
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d: d: d:
74 74 74
73 73 73
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d: d:
74 74
73 73
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41 41
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15
33 4
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d:
74
73
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41
1'
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d: d: d:
74 74 74
73 73 73
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41 41 41
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d: d:
74 74
73 73
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41 41
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41 46
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d:
74
73
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41
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44
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d:
74
73
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d: d:
74 74
73 73
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41 41
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d:
74
73
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41
1'
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d: d: d:
74 74 74
73 73 73
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41 41 41
1' 1' 1'
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4* 33 44
.5 .!! .'6
%a&el 8.3/ erhitungan jarak intercluster c4 dan c5 pada pengujian 5)cluster
d:
74
75
=1
41
31
36
1
.!
d:
74
75
=*
41
31
36
*
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d:
74
75
=4
41
31
35
!
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d:
74
75
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41
31
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14
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d: d:
74 74
75 75
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41 41
31 31
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d: d: d:
74 74 74
75 75 75
=' =! =1
41 41 33
31 31 11
33 * 36
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d:
74
75
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33
11
36
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d: d:
74 74
75 75
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33 33
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d:
74
75
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33
11
35
11
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d:
74
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33
11
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d: d:
74 74
75 75
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d:
74
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1
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d: d:
74 74
75 75
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d: d: d:
74 74 74
75 75 75
=3 =5 =6
31 31 31
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d:
74
75
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31
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33
13
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d:
74
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31
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d: d:
74 74
75 75
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46 46
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d:
74
75
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46
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35
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d: d: d:
74 74 74
75 75 75
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46 46 46
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d: d:
74 74
75 75
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74
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36
1
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d:
74
75
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35
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36
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d: d:
74 74
75 75
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d:
74
75
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35
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35
11
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d: d: d:
74 74 74
75 75 75
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35 35 35
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d: d:
74 74
75 75
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35 35
1 1
36 36
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d:
74
75
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35
1
35
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d: d:
74 74
75 75
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14 11
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d:
74
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35
1
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d:
74
75
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1
33
13
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d: d:
74 74
75 75
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1 33
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d:
74
75
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36
33
36
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d: d:
74 74
75 75
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36 36
33 33
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d: d: d:
74 74 74
75 75 75
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36 36 36
33 33 33
35 * 33
11 ' 13
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d:
74
75
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36
33
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d:
74
75
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4
36
36
1
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d: d:
74 74
75 75
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4 4
36 36
36 35
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d:
74
75
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4
36
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14
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74 74
75 75
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4 4
36 36
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d:
74
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36
33
13
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d: d:
74 74
75 75
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4 *'
36 *1
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d: d: d:
74 74 74
75 75 75
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=5
=6
='
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=
d: d:
74 74
75 75
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d:
74
75
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33
13
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d: d: d:
74 74 74
75 75 75
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* 36 36
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d: d:
74 74
75 75
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14 14
35 *3
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d:
74
75
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14
35
11
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d:
74
75
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14
*
'
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d: d:
74 74
75 75
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14 14
33 *
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d:
74
75
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36
1
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d: d: d:
74 74 74
75 75 75
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4! 4! 4!
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d: d:
74 74
75 75
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4! 4!
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35 *
11 '
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d:
74
75
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33
13
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d: d:
74 74
75 75
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d:
74
75
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*
36
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d:
74
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d: d:
74 74
75 75
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14 11
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d:
74
75
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3*
*
*
'
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d: d:
74 74
75 75
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33 *
13 '
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d: d: d:
74 74 74
75 75 75
=1 =* =4
41 41 41
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36 36 35
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d:
74
75
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41
1'
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14
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d:
74
75
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41
1'
35
11
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d: d:
74 74
75 75
=6 ='
41 41
1' 1'
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' 13
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d:
74
75
=!
41
1'
*
'
.35
=1
=11
=1*
=14
%a&el 8.40 erhitungan jarak intercluster c3 dan c5 pada pengujian 5)cluster
d:
73
d:
=1
75
=1
1
15
36
1
.6*
73
75
=*
1
15
36
*
.56
d:
73
75
=4
!
73
75
=3
*3
14
d: d:
73 73
75 75
=5 =6
15 15 15 15
35
d:
1 1 1 1
35 *
11 '
.'1 .1 .56 .5'
d: d:
73 73
75 75
=' =!
1
15
33 *
13 '
.34
1
15
d:
73
75
=1
d: d: d:
73 73 73
75 75 75
=* =4 =3
1* 1*
45 45
36
1
36 35 *3
* ! 14
1.13 .!6
1*
45
d: d:
73 73
75 75
=5 =6
1* 1* 1*
45 45 45
35 *
11 '
d:
73
75
='
d:
73
75
=!
1* 1*
45 45
33
13
*
'
d: d:
73 73
75 75
=1 =*
*1
46
*1 *1
46 46
36 36
1 *
d:
73
75
=4
35
!
d: d: d:
73 73 73
75 75 75
=3 =5 =6
*1
46
*1
46
*1 *1
46 46
*3 35 *
14 11 '
d: d:
73 73
75 75
=' =!
*1
46
33 *
13 '
d:
73
75
=1
*! *!
4 4
36
1
d: d:
73 73
75 75
=* =4
*! *! *!
4 4 4
36 35
* !
d:
73
75
=3
*3
14
d:
73
75
=5
35
11
d: d:
73 73
75 75
=6 ='
*!
4 4
' 13
.63
*!
* 33
d:
73
75
=!
'
75 75
=1 =*
4 *!
*
73 73
*! 4 4
*!
36 36
1 *
.63 1.45
d: d: d: d: d:
73 73 73
75 75 75
=4 =3 =5
4 4
*! *! *!
! 14 11
1.34 1.13
4
35 *3 35
d:
73
75
=6
'
73
75
='
*! *!
*
d:
4 4
33
13
1.31 1.*1
d: d:
73 73
75 75
=! =1
4
*! 33
* 36
' 1
1.31 1.4
d:
73
75
=*
*
73 73
75 75
=4 =3
33 33
36
d: d:
33
35 *3
! 14
1.5 1.46
d:
73
75
=5
11
73 73
75 75
=6 ='
33 33
35
d: d:
33
* 33
' 13
d: d: d:
73 73 73
75 75 75
=! =1 =*
15 15
33 4 4
* 36 36
' 1 *
=*
=4
=3
=5
=6
='
.5'
1.*1 .' 1.1 1.! 1. 1.! .3 .66 1. .53 . .!4 .' .!4 .'3 .33 .!1 .3' .' .5
1.3
1.41
1. 1.*' 1.*5 1.1! 1.*5 1.1 .!4
d: d:
73 73
75 75
=4 =3
15
4
35 *3
! 14
1.16
15
4
d:
73
75
=5
d: d: d:
73 73 73
75 75 75
=6 =' =!
15 15
4 4
35
11
* 33 *
' 13 '
1.6 1.1
15
4
d: d:
73 73
75 75
=1 =*
15 * *
4 3! 3!
36 36
1 *
d:
73
75
=4
d:
73
75
=3
* *
3! 3!
35
!
*3
14
d: d:
73 73
75 75
=5 =6
*
3!
* *
3! 3!
35 *
11 '
d:
73
75
='
33
13
d: d: d:
73 73 73
75 75 75
=! =1 =*
*
3!
*6
33
*6 *6
33 33
* 36 36
' 1 *
d: d:
73 73
75 75
=4 =3
*6
33
35 *3
! 14
d:
73
75
=5
*6 *6
33 33
35
11
d: d:
73 73
75 75
=6 ='
*6 *6
33 33 *6
* 33
' 13
d:
73
75
=!
*
'
d:
73
75
=1
36
1
d: d:
73 73
75 75
=* =4
*6 *6
* !
.!
36 35
d:
73
75
=3
14
=5 =6
*6 *6
*3
75 75
*6
35 *
11 '
.' 1.'
d: d:
73 73
d: d: d:
73 73 73
75 75 75
=' =! =1
*6 *6 4
13 ' 1
.6 1.1
*6
33 * 36
d:
73
75
=*
*
73
75
=4
4 4
36
d:
*6 *6
35
!
.6 .4
d: d:
73 73
75 75
=3 =5
*6 *6
4 4
*3 35
14 11
.53 .!4
d:
73
75
=6
'
73 73
75 75
=' =!
4 4
*
d: d:
*6 *6 *6
4
33 *
13 '
.'5 .'4
d:
73
75
=1
1
73 73
75 75
=* =4
41 41
36
d: d:
11 11 11
41
36 35
* !
d: d: d:
73 73 73
75 75 75
=3 =5 =6
11 11 11
41 41 41
*3 35 *
14 11 '
=!
=
=1
=11
=1*
.'4
.6 1.1 .!! .63 .4 .6' .!3 .'5 .'5 .'5 .1 .65 .6 .5! .!' .'! .'' .'! 1.1* 1.*
1.1
.!'
.'5 1.14 .!4 1.* .'! 1.! 1.!
d: d:
73 73
75 75
=' =!
11
41
33 *
13 '
.!
11
41
d:
73
75
=1
d: d: d:
73 73 73
75 75 75
=* =4 =3
' '
46 46
36
1
36 35 *3
* ! 14
1.4 1.*
'
46
d: d:
73 73
75 75
=5 =6
' ' '
46 46 46
35 *
11 '
d:
73
75
='
d:
73
75
=!
' '
46 46
33
13
*
'
d: d:
73 73
75 75
=1 =*
*
44
* *
44 44
36 36
1 *
d:
73
75
=4
35
!
d: d: d:
73 73 73
75 75 75
=3 =5 =6
*
44
*
44
* *
44 44
*3 35 *
14 11 '
d: d:
73 73
75 75
=' =!
*
44
33 *
13 '
d:
73
75
=1
! !
13 13
36
1
d: d:
73 73
75 75
=* =4
! ! !
13 13 13
36 35
* !
d:
73
75
=3
*3
14
d:
73
75
=5
35
11
d: d:
73 73
75 75
=6 ='
!
13 13
' 13
.
!
* 33
d:
73
75
=!
'
75 75
=1 =*
13 3
*
73 73
! ! !
3
36 36
1 *
. 1.4
d: d: d: d: d:
73 73 73
75 75 75
=4 =3 =5
! !
3 3 3
! 14 11
1.46 1.1
!
35 *3 35
d:
73
75
=6
'
73
75
='
3 3
*
d:
! !
33
13
1.*' 1.1'
d: d:
73 73
75 75
=! =1
! *4
3 5
* 36
' 1
1.*' 1.
d:
73
75
=*
*
73 73
75 75
=4 =3
5 5
36
d: d:
*4 *4 *4
5
35 *3
! 14
.'6 1.5
d:
73
75
=5
11
73 73
75 75
=6 ='
5 5
35
d: d:
*4 *4 *4
5
* 33
' 13
d: d: d:
73 73 73
75 75 75
=! =1 =*
*4 ** **
5 3* 3*
* 36 36
' 1 *
=14
=13
=15
=16
=1'
=1!
1.!
1.4' 1.* 1.*6 1.* 1.1' 1.* .'6 .3' .!4 .54 .'* .65 .61 .65 .!' .!! .' .53 .!* .6
1.3
1.*'
.61 .6 .!' .!! .!' .' .'1
d: d:
73 73
75 75
=4 =3
**
3*
**
3*
d:
73
75
=5
d: d: d:
73 73 73
75 75 75
=6 =' =!
** **
3* 3*
**
3*
d: d:
73 73
75 75
=1 =*
** *1 *1
3* 4* 4*
d:
73
75
=4
d:
73
75
=3
*1 *1
d: d:
73 73
75 75
=5 =6
d:
73
75
='
d: d: d:
73 73 73
75 75 75
=! =1 =*
d: d:
73 73
75 75
=4 =3
d:
73
75
=5
d: d:
73 73
75 75
=6 ='
d:
73
75
=!
d:
73
75
=1
d: d:
73 73
75 75
d:
73
d: d:
73 73
d: d:
73 73
=1
=*
=*1
35 *3
! 14
1.*
35
11
* 33 *
' 13 '
.4 .!5
36 36
1 *
4* 4*
35
!
*3
14
*1
4*
*1 *1
4* 4*
35 *
11 '
33
13
*1
4*
1*
33
1* 1*
33 33
* 36 36
' 1 *
1*
33
35 *3
! 14
1* 1*
33 33
35
11
1* 1* 1*
33 33 44
* 33
' 13
*
'
36
1
=* =4
1*
44 44
* !
.!4
1*
36 35
75
=3
14
=5 =6
44 44
*3
75 75
1* 1* 1*
44
35 *
11 '
.'' 1.!
75 75
=' =!
1* 1*
44 44
33 *
13 '
erhitungan kemudian dilanjutkan dngan mencari nilai
.5'
.!4 .!5 . .6 .6 .3 .!5 .! .'5 .! 1.** .6 1.*' .!! 1.1! 1.13 1. 1.13 1.1* 1.1
1.6 .! 1.6
minimum
intercluster dari masing)masing perbandingan cluster yang sudah dicari sebelumnya.
$erikut
merupakan
intercluster . Cilai min d(c1.c*" : .'1 Cilai min d(c1.c4" : .'5 Cilai min d(c1.c3" : .6 Cilai min d(c1.c5" : .3 Cilai min d(c*.c4" : .'4 Cilai min d(c*.c3" : .
hasil
dari
perhitungan
nilai
minimum
Cilai min d(c*.c5" : .5 Cilai min d(c4.c3" : .11 Cilai min d(c4.c5" : .1 Cilai min d(c3.c5" : .1
8.5.3 *e)+itu,a Ide!s Da"ies#$ouldi 5# cluster
erhitungan #ndeks Davies)$ouldin pada pengujian 5)cluster dimulai dengan pencarian nilai ma2 dengan rumus<
$erikut
merupakan
hasil
pencarian
ma2
pada
masing)masing
perbandingan cluster yang ada pada pengujian data sampel 5)cluster .
7ontoh perhitungan nilai ma2<
erbandingan nilai ma2 d(c1,c*" < d(c1,c4"
?a2 E(4.* / 4.15"F : 4.* erhitungan tersebut akan melibatkan data perhitungan nilai minimum jarak intercluster dan maksimum jarak intracluster pada pengujian 5)cluster sebelumnya. $erikut perhitungan keseluruhan nilai ma2 pada pengujian 5) cluster yang ditampilkan secara sederhana pada tabel !.*4.
%a&el 8.41 erhitungan nilai ma2 pada pengujian 5)cluster
*e)+itu,a Ma!s
d(c1,c*"
d(c1,c4" d(c1,c3" d(c1,c5"
4.* 4.* 4.*
4.15 3.3' 3.64
*e)&adi,a MA 4.* 3.3' 3.64
d(c1,c4"
d(c1,c3"
d(c1,c5"
d(c*,c4"
d(c*,c3"
d(c*,c5" d(c4,c3" d(c4,c5"
d(c*,c4" d(c*,c3" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5"
4.* 4.* 4.* 4.* 4.* 4.*
*.'' *6. *.4 1'.35 151. .64
4.* *6. 4.* 1'.35 151. .64
d(c1,c3"
4.15
3.3'
3.3'
d(c1,c5" d(c*,c4" d(c*,c3" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c1,c5" d(c*,c4" d(c*,c3" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c*,c4" d(c*,c3" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c*,c3" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c*,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c4,c3" d(c4,c5" d(c3,c5" d(c4,c5" d(c3,c5" d(c3,c5"
4.15 4.15 4.15 4.15 4.15 4.15 4.15 3.3' 3.3' 3.3' 3.3' 3.3' 3.3' 3.3' 3.64 3.64 3.64 3.64 3.64 3.64 *.'' *.'' *.'' *.'' *.'' *6. *6. *6. *6. *.4 *.4 *.4 1'.35 1'.35 151.
3.64 *.'' *6. *.4 1'.35 151. .64 3.64 *.'' *6. *.4 1'.35 151. .64 *.'' *6. *.4 1'.35 151. .64 *6. *.4 1'.35 151. .64 *.4 1'.35 151. .64 1'.35 151. .64 151. .64 .64
3.64 4.15 *6. 4.15 1'.35 151. .64 3.64 3.3' *6. 3.3' 1'.35 151. .64 3.64 *6. 3.64 1'.35 151. .64 *6. *.'' 1'.35 151. .64 *6. *6. 151. *6. 1'.35 151. .64 151. 1'.35 151.
