8.1 Uji Va Validitas liditas Cluster Indeks Indeks DaviesDavies-Bould Bouldin in
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 $ouldin n pada pada tahun tahun 1', 1', dan diguna digunakan kan untuk untuk mengev mengevalua aluasi si algoritma clustering. enggunaan enggunaan indeks indeks validitas validitas Davies)$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 perhit itun unga gan n jarak jarak clus cluste terr meng menggu guna naka kan n #nde #ndeks ks Davi Davies es $ouldin $ouldin ini terdapat terdapat * tahap yang digunakan yaitu perhitungan perhitungan jarak intracluster intracluster dan perhitungan jarak intercluster. engukuran dengan metode ini bertujuan untuk memaksimalkan jarak intercluster antara salah satu cluster dengan cluster yang lain lain (separ (separatio ation n value" value" sekalig sekaligus us memini meminimal malkan kan jarak jarak intrac intraclus luster ter antara antara titik titik dalam sebuah cluster (compactness value" ($olshakova + -uaje ** / 0unter + $unke **". $erikut merupakan contoh penerapan perhitungan indeks Davies)$ouldin pada cluster K)medoids dengan data objek seperti pada table !.1. Table 8.1 Data bjek 2luster K)medoids
data 1 * 5 4 6 7 ' ! 1 11
3 4 1 1* * 47 51 *1 *! 5 47 14
y 55 16 56 7 1 41 57 5 *! * *!
1* 15 14 16 17 1' 1! 1 * *1 ** *5 *4 *6 *7 *' *! * 5 51 5* 55 54 56 57 5' 5! 5 4 41 4* 45 44 46 47 4' 4! 4 6
44 41 46 *4 57 16 46 7 * *7 46 47 *7 11 ' 1* 5 * *' ! 46 * *' 44 1 ! *5 1 ** *1 * * 5! 1* 4* 1* 51
11 *4 ! 44 15 1' 5 *! 5' 4! 44 1 *7 44 5 51 57 7 47 55 *1 14 11 ' 15 14 56 4 6 1 4* 5* ' 5! * 44 * 55 1'
erh erhit itun unga gan n jarak jarak pada pada uji uji coba coba inde indeks ks Davi Davies) es)$o $oul uldi din n digu diguna naka kan n perhitungan jarak 2anberra Distance, untuk setiap nilai dari * vektor yang akan dicocokkan dicocokkan,, Canberra distance distance membagi absolute selisih absolute selisih * nilai dengan jumlah
1* 15 14 16 17 1' 1! 1 * *1 ** *5 *4 *6 *7 *' *! * 5 51 5* 55 54 56 57 5' 5! 5 4 41 4* 45 44 46 47 4' 4! 4 6
44 41 46 *4 57 16 46 7 * *7 46 47 *7 11 ' 1* 5 * *' ! 46 * *' 44 1 ! *5 1 ** *1 * * 5! 1* 4* 1* 51
11 *4 ! 44 15 1' 5 *! 5' 4! 44 1 *7 44 5 51 57 7 47 55 *1 14 11 ' 15 14 56 4 6 1 4* 5* ' 5! * 44 * 55 1'
erh erhit itun unga gan n jarak jarak pada pada uji uji coba coba inde indeks ks Davi Davies) es)$o $oul uldi din n digu diguna naka kan n perhitungan jarak 2anberra 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<
2ontoh < Untuk vektor dan $ adalah sebagai berikut <
Canberra distance)nya distance )nya adalah <
8.2 Uji Validitas Indeks Davies-Bouldin 2-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.
Gambar 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. Tabel 8.2 Data >ample Cluster 1
=1 =* =5 =4 =6 =7 ='
CLUSTER 1 47 51 47 44 41 46 57
1 41 * 11 *4 ! 1'
=! = =1 =11 =1* =15 =14 =16 =17 =1'
46 * 46 47 5 46 * 44 * 5!
*! 4! 1 44 47 11 ' 14 ' *
=1!
51
1'
Tabel 8. Data >ample Cluster 1*
CLUSTER * =1 4 =* 1* =5 * =4 *1 =6 *! =7 5 =' 14 =! = *4 =1 16 =11 7 =1* *7 =15 =14 *7 =16 11 =17 ' =1' 1*
55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7
=1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*'
*1 14 15 56 4 6 1 4* 5* 5!
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8.2.1 !er"itun#an $arak Intracluster 2-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 matri3 2anberra Distance, maka perhitungannya adalah sebagai berikut. ;umus 2anbbera Distance <
Tabel 8.% erhitungan Intracluster ada Cluster 1
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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 2anbbera 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. Tabel 8.& erhitungan Intracluster ada Cluster *
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d@c* d@c*
=*7 =*'
=* =*!
*1 *
5* 5!
1* 1*
55 44
.*' .'1
d@c*
=*'
=*
*
5!
1*
55
.'1
d@c*
=*!
=*
1*
44
1*
55
.
=abel !.6 merupakan perhitungan untuk menghitung intracluster jarak pada cluster *, dihitung menggunakan jarak matrik 2anberra, 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,=4", (=1,17", (=5,=14", (=1,=11" yang memiliki nilai jarak .*5 dan cluster * yaitu pada jarak (=6,=*1" yang memiliki nilai jarak ,5.
8.2.2 !er"itun#an $arak Intercluster 2-cluster
>etelah melakukan perhitungan jarak intracluster , 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 2anberra Distance. ada perhitungan jarak intercluster agar perhitungannya terlihat lebih jelas, dapat dilihat perhitungannya sebagai berikut. Tabel 8.' erhitungan Jarak Intercluster ada Cluster 1 dan Cluster *
d
c1
=1
c*
=1
47
1
4
55
.!5
d
c1
=1
c*
=*
47
1
1*
6
.6!
d
c1
=1
c*
=5
47
1
*
7
.1
d
c1
=1
c*
=4
47
1
*1
57
.5'
d
c1
=1
c*
=6
47
1
*!
5
.*4
d
c1
=1
c*
=7
47
1
5
*!
.!'
d
c1
=1
c*
='
47
1
14
*!
.65
d
c1
=1
c*
=!
47
1
44
.7'
d d
c1 c1
=1 =1
c* c*
= =1
47 47
1 1
*4 16
15 5
.51 .6
d d d d d
c1 c1 c1 c1 c1
=1 =1 =1 =1 =1
c* c* c* c* c*
=11 =1* =15 =14 =16
47 47 47 47 47
1 1 1 1 1
7 *7 *7 11
5' 44 *7 5 51
.'7 .*! .7' .*! .71
d d d
c1 c1 c1
=1 =1 =1
c* c* c*
=17 =1' =1!
47 47 47
1 1 1
' 1* *'
57 7 *1
.'5 .6! .*7
d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=1 =1 =1 =1 =1 =1 =1 =1 =1 =1
c* c* c* c* c* c* c* c* c* c*
=1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
47 47 47 47 47 47 47 47 47 47
1 1 1 1 1 1 1 1 1 1
! *' 1 ! *5 1 ** *1 * 1*
14 15 56 4 6 1 4* 5* 5! 44
.' .*7 .6 .' .55 .4 .56 .5' .1 .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
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
=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* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
47 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51
1 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
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.6! .'' .45 .!7 .1 .6 .!* .5! .66 .15 .56 .7' . .66 . .4' .75 .45 .' .6! .' .4 .6 .16 .1 .1' .1 .!! .44
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
=* =5 =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =* =*
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
51 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47
41 * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.44 .!4 .6! .1 .5' .*4 .!' .65 .7' .51 .61 .'7 .*! .7' .*! .71 .'5 .6! .*7 .' .*7 .6 .' .55 .4 .56 .5' .1 .6!
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
=* =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4
c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1*
47 44 44 44 44 44 44 44 44 44 44 44 44
* 11 11 11 11 11 11 11 11 11 11 11 11
1* 4 1* * *1 *! 5 14 *4 16 7 *7
55 55 6 7 57 5 *! *! 44 15 5 5' 44
.6! .!* .6' .1 .56 .** .!7 .61 .76 .* .4 .'6 .*6
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
=4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4 =4
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44
11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
*7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
*7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.77 .*7 .6 .'* .6' .*4 .7 .*4 .4 .7! .51 .4 .55 .56 . .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
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 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6 =6
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6
44 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
11 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4 *4
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 **
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4*
.6' .!* .64 .! .5* .1 .!7 .4 .74 .*7 .47 .'4 .** .74 .** .6! .'1 .64 .*1 .7' .* .6 .7' .*! .5 .5
d d d
c1 c1 c1
=6 =6 =6
c* c* c*
=*7 =*' =*!
41 41 41
*4 *4 *4
*1 * 1*
5* 5! 44
.5* . .64
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
=6 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7 =7
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
41 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46
*4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.66 .!5 .6! .1 .57 .*5 .!7 .6* .77 .5 .4 .'7 .*' .77 .*' .7 .'* .6! .*6 .7 .*6 .4 .7 .5* .4 .54 .57 . .6'
d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=7 =' =' =' =' =' =' =' =' ='
c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! =
46 57 57 57 57 57 57 57 57 57
! 1' 1' 1' 1' 1' 1' 1' 1' 1'
1* 4 1* * *1 *! 5 14 *4
55 55 6 7 57 5 *! *! 44 15
.6' .' .4 .!! .*7 .1* .!4 .44 .6 .*
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
=' =' =' =' =' =' =' =' =' =' =' =' =' =' =' =' =' =' ='
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.41 .'1 .17 .7 .17 .65 .7' .6 .14 .75 .14 .4 .75 .** .* .*4 .*7 .! .6
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
=' =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =! =!
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =**
57 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46
1' *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *! *!
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 !
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4
.6 .!4 .6' . .57 .*5 .!! .65 .77 .5 .6 .'7 .*' .7' .*' .71 .'5 .6' .*6 .7 .*6 .6 .'
d d d d d d
c1 c1 c1 c1 c1 c1
=! =! =! =! =! =!
c* c* c* c* c* c*
=*5 =*4 =*6 =*7 =*' =*!
46 46 46 46 46 46
*! *! *! *! *! *!
*5 1 ** *1 * 1*
6 1 4* 5* 5! 44
.5* .4 .54 .57 .1 .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
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*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
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! 4! 4! 4! 4!
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.6! .'6 .41 .!6 .17 .* .!1 .56 .65 . .5* .76 .6 .6* .6 .46 .71 .41 .4 .67 .4 .5 .6' .1* . .14 .17 .!' .41
d d d d d d d
c1 c1 c1 c1 c1 c1 c1
= =1 =1 =1 =1 =1 =1
c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7
* 46 46 46 46 46 46
4! 1 1 1 1 1 1
1* 4 1* * *1 *! 5
55 55 6 7 57 5 *!
.41 .!5 .6' . .57 .*5 .!'
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
=1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1 =1
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
*! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.6* .77 .5 .6 .'7 .*' .77 .*' .7 .'5 .6' .*6 .' .*6 .6 .7 .5* .4 .54 .57 .1 .6'
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
=1 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11 =11
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1
46 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47
1 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' !
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14
.6! .!4 .6! . .5' .*4 .!' .65 .7' .51 .61 .'' .*! .7' .*! .71 .'5 .6! .*7 .'
d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1
=11 =11 =11 =11 =11 =11 =11 =11 =11
c* c* c* c* c* c* c* c* c*
=* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
47 47 47 47 47 47 47 47 47
44 44 44 44 44 44 44 44 44
*' 1 ! *5 1 ** *1 * 1*
15 56 4 6 1 4* 5* 5! 44
.*7 .7 .' .55 .4 .56 .5' .* .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
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
=11 =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*
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
47 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 5
44 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.6! .!1 .6* .! .5 .17 .!6 .4' .7* .*4 .44 .'5 .* .7* .* .67 .7 .6* .1! .76 .1! .6 .77 .*7 .5 .*! .5 . .65
d d d d
c1 c1 c1 c1
=1* =1* =1* =1*
c* c* c* c*
=* =1 =* =5
5 5 5 5
47 47 47 47
1* 4 1* *
55 55 6 7
.65 .!1 .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
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* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =1* =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*
=4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
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
47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47
*1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.5 .17 .!6 .4' .7* .*4 .44 .'5 .* .7* .* .67 .7 .6* .1! .76 .1! .6 .77 .*7 .5 .*! .5 . .65
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
=1* =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17
5 * * * * * * * * * * * * * * * *
47 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 '
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57
.65 .'4 .41 .!' .17 .* .! .54 .6* . .51 .74 .6 .6* .6 .44 .7
d d d d d d d d d d d d
c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1 c1
=14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14 =14
c* c* c* c* c* c* c* c* c* c* c* c*
=1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
* * * * * * * * * * * *
' ' ' ' ' ' ' ' ' ' ' '
1* *' ! *' 1 ! *5 1 ** *1 * 1*
7 *1 14 15 56 4 6 1 4* 5* 5! 44
.41 .4 .67 .4 .1 .67 .11 .1 .14 .17 .!6 .41
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
=14 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16 =16
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
* 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44
' 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
1* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.41 .!5 .6' .1 .56 .** .!' .61 .76 .* .4 .'6 .*7 .77 .*7 .7 .'* .6' .*4 .7 .*4 .6 .7 .51 .4 .55 .56 . .6'
d
c1
=16
c*
=*
44
14
1*
55
.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
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
=17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17 =17
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
* * * * * * * * * * * * * * * * * * * * * * * * * * * *
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.'4 .41 .!' .17 .* .! .54 .6* . .51 .74 .6 .6* .6 .44 .7 .41 .4 .67 .4 .1 .67 .11 .1 .14 .17 .!6 .41
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
=17 =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1'
c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=* =1 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15
* 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5!
' * * * * * * * * * * * * *
1* 4 1* * *1 *! 5 14 *4 16 7 *7
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7
.41 .! .61 .! .* .16 .!6 .47 .71 .*5 .45 .'* .1 .7*
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
=1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1' =1'
c* c* c* c* c* c* c* c* c* c* c* c* c* c* c*
=14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7 =*' =*!
5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5! 5!
* * * * * * * * * * * * * * *
*7 11 ' 1* *' ! *' 1 ! *5 1 ** *1 * 1*
5 51 57 7 *1 14 15 56 4 6 1 4* 5* 5! 44
.1 .66 .7! .61 .1' .76 .1' .4 .76 .*4 .5 .*' .* .! .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
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' =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!
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 =* =5 =4 =6 =7 =' =! = =1 =11 =1* =15 =14 =16 =17 =1' =1! =1 =* =*1 =** =*5 =*4 =*6 =*7
5! 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51
* 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* 4 1* * *1 *! 5 14 *4 16 7 *7 *7 11 ' 1* *' ! *' 1 ! *5 1 ** *1
55 55 6 7 57 5 *! *! 44 15 5 5' 44 *7 5 51 57 7 *1 14 15 56 4 6 1 4* 5*
.6* .'7 .44 .!' .1 .6 .!* .5! .64 .15 .54 .7' . .66 . .4' .75 .44 .' .6 .' .5 .6! .16 .1 .1' .1
d d
c1 c1
=1! =1!
c* c*
=*' =*!
51 51
1' 1'
* 1*
5! 44
.!' .44
d
c1
=1!
c*
=*
51
1'
1*
55
.44
=abel 4 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((47,1",(4,55""
:
B
?aka jarak yang didapat dari perhitungan jarak 2anbbera adalah .!5 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.
8.2. !er"itun#an Indeks Davies Bouldin 2-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 .6''565'.
8. Uji Validitas Indeks Davies-Bouldin -cluster
Data sample yang digunakan pada pengujian validitas indeks Davies) $ouldin pada 5)cluster ditunjukkan pada table !.6
Tabel 8.& Data sample 5)cluster
cluster 1
cluster 2
cluster
4
55
47
1
51
41
5
*!
51
41
7
5'
47
*
1 1*
16 56
*7
44
11
*1
57
' !
57 14
46 *4
! 15
*
5!
57 46 1*
1' 1 7
*! 14 41
5 *! *4
44
46
11
16 46
5 *!
* *'
' 15
*
4!
44
14
*7 47
44 44
*
'
*7
5
11 5
51 47
*
55
*'
*1
1 ! *5
56 4 6
1 **
1 4*
*1
5*
5! 1*
* 44
4*
*
1*
55
51
1'
ersebaran data sample yang diujikan pada algoritma k)medoids 5 cluster dapat dilihat pada gambar !.*
