8.1
8.1 Uji VUji Vaaliditaliditas Cluster Is Cluster Indeks Davndeks Davies-ies-BouldBouldinin Uj
Uji i vavalilididitastas clustercluster digundigunakan untuk akan untuk mengmengevaluasevaluasi i hasil dari hasil dari analianalisissis cluster
cluster secasecara ra kuakuantintitatitatif f sehsehingingga ga dihdihasiasilkalkan n kelkelompompok ok optoptimaimal. l. KelKelomompok pok optimal adalah kelompok yang mempunyai jarak yang padat antar individu dalam optimal adalah kelompok yang mempunyai jarak yang padat antar individu dalam kelompok dan terisolasi dari kelompok lain dengan baik (Dubes and Jain, 1!!". kelompok dan terisolasi dari kelompok lain dengan baik (Dubes and Jain, 1!!".
#ndek
#ndeks s DavieDavies s $oul$ouldin (D$#" din (D$#" diperdiperkenalkkenalkan an oleh David oleh David %. Davies %. Davies dandan Don
Donald ald &&. . $ou$ouldildin n padpada a tahtahun un 1'1', , dan dan digdigunaunakan kan untuntuk uk menmengevgevaluaaluasisi algoritma clustering.
algoritma clustering. engg
enggunaan unaan indekindeks s validvaliditas itas DaviesDavies)$oul)$ouldin din dapat dapat mengmengidentiidentifikasikfikasikanan cluster
cluster yang padat ( yang padat (compact tcluster compact tcluster " dan terpisah dengan baik terh" dan terpisah dengan baik terhadapadap cluster cluster yang lain (
yang lain (Well-Separated Well-Separated " seperti halnya pada indeks validitas Dunn" seperti halnya pada indeks validitas Dunn
a
ada da peperhrhititunungagan n jajarak rak clclususteter r memengnggugunanakakan n #n#ndedeks ks DaDavivieses $oul
$ouldin ini din ini terdapterdapat at * * tahap yang digunakan yaitu perhituntahap yang digunakan yaitu perhitungan jarak gan jarak intraclintracluster uster dan perhitungan jarak intercluster. engukuran dengan metode ini bertujuan untuk dan perhitungan jarak intercluster. engukuran dengan metode ini bertujuan untuk memaksimalkan jarak intercluster antara salah satu cluster dengan cluster yang memaksimalkan jarak intercluster antara salah satu cluster dengan cluster yang lai
lain n (se(separparatioation n valvalue" ue" sekasekaligligus us memmeminiinimalmalkan kan jarajarak k intintracraclusluster ter antantara ara tittitik ik dalam sebuah cluster (compactness
dalam sebuah cluster (compactness value" ($olshakova + -uaje ** / 0unter +value" ($olshakova + -uaje ** / 0unter + $unke **".
$unke **".
$erikut merupakan contoh penerapan perhitungan indeks Davies)$ouldin $erikut merupakan contoh penerapan perhitungan indeks Davies)$ouldin pada cluster K)medoids dengan data objek seperti pada table !.1.
pada cluster K)medoids dengan data objek seperti pada table !.1. Table 8.1
Table 8.1 Data bjek Data bjek 2luster K)medoids2luster K)medoids
d daattaa 33 yy 1 1 44 5555 * * 11 1166 5 5 11** 5566 4 4 ** 77 6 6 4477 11 7 7 5511 4411 ' ' **11 5577 ! ! **!! 55 55 **!! 1 1 4477 ** 1 111 1144 **!!
1 1** 4444 1111 1 155 4411 **44 1 144 4466 !! 1 166 4444 1 177 **44 1155 1 1'' 5577 11'' 1 1!! 1166 55 1 1 4466 **!! * * 77 55'' * *11 ** 44!! * *** **77 4444 * *55 4466 11 * *44 **77 * *66 4477 4444 * *77 **77 55 * *'' 1111 5511 * *!! '' 5577 * * 11** 77 5 5 55 4477 5 511 ** 5555 5 5** **'' **11 5 555 !! 1144 5 544 4466 1111 5 566 ** '' 5 577 **'' 1155 5 5'' 4444 1144 5 5!! 11 5566 5 5 !! 44 4 4 **55 66 4 411 11 11 4 4** **** 44** 4 455 **11 55** 4 444 ** '' 4 466 ** 55!! 4 477 55!! ** 4 4'' 11** 4444 4 4!! 44** ** 4 4 11** 5555 6 6 5511 11'' e
erhrhititunungagan n jajarak rak papada da ujuji i cocoba ba inindedeks ks DaDavivies)es)$o$oululdidin n didigugunanakakann perhitungan
perhitungan jarak jarak 2anberra 2anberra Distance, Distance, untuk untuk setiap setiap nilai nilai dari dari * * vektor vektor yang yang akanakan dicoc
1 1** 4444 1111 1 155 4411 **44 1 144 4466 !! 1 166 4444 1 177 **44 1155 1 1'' 5577 11'' 1 1!! 1166 55 1 1 4466 **!! * * 77 55'' * *11 ** 44!! * *** **77 4444 * *55 4466 11 * *44 **77 * *66 4477 4444 * *77 **77 55 * *'' 1111 5511 * *!! '' 5577 * * 11** 77 5 5 55 4477 5 511 ** 5555 5 5** **'' **11 5 555 !! 1144 5 544 4466 1111 5 566 ** '' 5 577 **'' 1155 5 5'' 4444 1144 5 5!! 11 5566 5 5 !! 44 4 4 **55 66 4 411 11 11 4 4** **** 44** 4 455 **11 55** 4 444 ** '' 4 466 ** 55!! 4 477 55!! ** 4 4'' 11** 4444 4 4!! 44** ** 4 4 11** 5555 6 6 5511 11'' e
erhrhititunungagan n jajarak rak papada da ujuji i cocoba ba inindedeks ks DaDavivies)es)$o$oululdidin n didigugunanakakann perhitungan
perhitungan jarak jarak 2anberra 2anberra Distance, Distance, untuk untuk setiap setiap nilai nilai dari dari * * vektor vektor yang yang akanakan dicoc
dari absolute * nilai tersebut. 8asil dari setiap dua nilai yang dicocokkan lalu dari absolute * nilai tersebut. 8asil dari setiap dua nilai yang dicocokkan lalu dijumlahkan untuk mendapatkan
dijumlahkan untuk mendapatkan Canberra distanceCanberra distance. Jika kedua koordinat nol)nol. Jika kedua koordinat nol)nol ki
kita ta memembmbererikikan an dedefifininisi si dedengngan an 99 : : .. Distance Distance ini sangat peka terhadap ini sangat peka terhadap sediki
sedikit t perubperubahan dengan kedua koordinat mendekahan dengan kedua koordinat mendekati ati nol. ;umus darinol. ;umus dari CanberraCanberra distance
distance<<
2ontoh < Untuk vektor
2ontoh < Untuk vektor dan $ adalah sebagai dan $ adalah sebagai berikut <berikut <
Canberra distance
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 8.1Data >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 CLUSTER 1 =1 47 1 =* 51 41 =5 47 * =4 44 11 =6 41 *4 =7 46 ! =' 57 1'
=! 46 *! = * 4! =1 46 1 =11 47 44 =1* 5 47 =15 46 11 =14 * ' =16 44 14 =17 * ' =1' 5! * =1! 51 1'
Tabel 8. Data >ample Cluster 1* CLUSTER * =1 4 55 =* 1* 6 =5 * 7 =4 *1 57 =6 *! 5 =7 5 *! =' 14 *! =! 44 = *4 15 =1 16 5 =11 7 5' =1* *7 44 =15 *7 =14 *7 5 =16 11 51 =17 ' 57 =1' 1* 7 =1! *' *1 =1 ! 14 =* *' 15 =*1 1 56 =** ! 4 =*5 *5 6 =*4 1 1 =*6 ** 4* =*7 *1 5* =*' * 5!
=*! 1* 44
=* 1* 55
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
d@c1 =1 =* 47 1 51 41 .1 d@c1 =1 =5 47 1 47 * . d@c1 =1 =4 47 1 44 11 .* d@c1 =1 =6 47 1 41 *4 .7 d@c1 =1 =7 47 1 46 ! .1 d@c1 =1 =' 47 1 57 1' .1* d@c1 =1 =! 47 1 46 *! .1 d@c1 =1 = 47 1 * 4! .** d@c1 =1 =1 47 1 46 1 .1 d@c1 =1 =11 47 1 47 44 . d@c1 =1 =1* 47 1 5 47 .! d@c1 =1 =15 47 1 46 11 .1 d@c1 =1 =14 47 1 * ' .*5 d@c1 =1 =16 47 1 44 14 .* d@c1 =1 =17 47 1 * ' .*5 d@c1 =1 =1' 47 1 5! * . d@c1 =1 =1! 47 1 51 1' .1 d@c1 =* =5 51 41 47 * .1 d@c1 =* =4 51 41 44 11 .1'
d@c1 =* =6 51 41 41 *4 .14 d@c1 =* =7 51 41 46 ! .1! d@c1 =* =' 51 41 57 1' .' d@c1 =* =! 51 41 46 *! .1! d@c1 =* = 51 41 * 4! .5 d@c1 =* =1 51 41 46 1 .1! d@c1 =* =11 51 41 47 44 .1 d@c1 =* =1* 51 41 5 47 .11 d@c1 =* =15 51 41 46 11 .1! d@c1 =* =14 51 41 * ' .5 d@c1 =* =16 51 41 44 14 .1' d@c1 =* =17 51 41 * ' .5 d@c1 =* =1' 51 41 5! * .1 d@c1 =* =1! 51 41 51 1' . d@c1 =5 =4 47 * 44 11 .* d@c1 =5 =6 47 * 41 *4 .7 d@c1 =5 =7 47 * 46 ! .1 d@c1 =5 =' 47 * 57 1' .1* d@c1 =5 =! 47 * 46 *! .1 d@c1 =5 = 47 * * 4! .*5 d@c1 =5 =1 47 * 46 1 .1 d@c1 =5 =11 47 * 47 44 . d@c1 =5 =1* 47 * 5 47 .! d@c1 =5 =15 47 * 46 11 .1 d@c1 =5 =14 47 * * ' .*5 d@c1 =5 =16 47 * 44 14 .* d@c1 =5 =17 47 * * ' .*5 d@c1 =5 =1' 47 * 5! * .1 d@c1 =5 =1! 47 * 51 1' .1 d@c1 =4 =6 44 11 41 *4 .4 d@c1 =4 =7 44 11 46 ! .1 d@c1 =4 =' 44 11 57 1' .1 d@c1 =4 =! 44 11 46 *! .1 d@c1 =4 = 44 11 * 4! .* d@c1 =4 =1 44 11 46 1 .1 d@c1 =4 =11 44 11 47 44 .* d@c1 =4 =1* 44 11 5 47 .7 d@c1 =4 =15 44 11 46 11 .1 d@c1 =4 =14 44 11 * ' .* d@c1 =4 =16 44 11 44 14 .
d@c1 =4 =17 44 11 * ' .* d@c1 =4 =1' 44 11 5! * .' d@c1 =4 =1! 44 11 51 1' .1' d@c1 =6 =7 41 *4 46 ! .6 d@c1 =6 =' 41 *4 57 1' .7 d@c1 =6 =! 41 *4 46 *! .6 d@c1 =6 = 41 *4 * 4! .1' d@c1 =6 =1 41 *4 46 1 .6 d@c1 =6 =11 41 *4 47 44 .7 d@c1 =6 =1* 41 *4 5 47 .* d@c1 =6 =15 41 *4 46 11 .6 d@c1 =6 =14 41 *4 * ' .1' d@c1 =6 =16 41 *4 44 14 .4 d@c1 =6 =17 41 *4 * ' .1' d@c1 =6 =1' 41 *4 5! * .4 d@c1 =6 =1! 41 *4 51 1' .14 d@c1 =7 =' 46 ! 57 1' .11 d@c1 =7 =! 46 ! 46 *! . d@c1 =7 = 46 ! * 4! .*1 d@c1 =7 =1 46 ! 46 1 . d@c1 =7 =11 46 ! 47 44 .1 d@c1 =7 =1* 46 ! 5 47 .' d@c1 =7 =15 46 ! 46 11 . d@c1 =7 =14 46 ! * ' .** d@c1 =7 =16 46 ! 44 14 .1 d@c1 =7 =17 46 ! * ' .** d@c1 =7 =1' 46 ! 5! * .! d@c1 =7 =1! 46 ! 51 1' .1! d@c1 =' =! 57 1' 46 *! .11 d@c1 =' = 57 1' * 4! .11 d@c1 =' =1 57 1' 46 1 .11 d@c1 =' =11 57 1' 47 44 .1* d@c1 =' =1* 57 1' 5 47 .4 d@c1 =' =15 57 1' 46 11 .11 d@c1 =' =14 57 1' * ' .11 d@c1 =' =16 57 1' 44 14 .1 d@c1 =' =17 57 1' * ' .11 d@c1 =' =1' 57 1' 5! * .5 d@c1 =' =1! 57 1' 51 1' .' d@c1 =! = 46 *! * 4! .**
d@c1 =! =1 46 *! 46 1 . d@c1 =! =11 46 *! 47 44 .1 d@c1 =! =1* 46 *! 5 47 .' d@c1 =! =15 46 *! 46 11 . d@c1 =! =14 46 *! * ' .*1 d@c1 =! =16 46 *! 44 14 .1 d@c1 =! =17 46 *! * ' .*1 d@c1 =! =1' 46 *! 5! * .! d@c1 =! =1! 46 *! 51 1' .1! d@c1 = =1 * 4! 46 1 .*1 d@c1 = =11 * 4! 47 44 .*5 d@c1 = =1* * 4! 5 47 .16 d@c1 = =15 * 4! 46 11 .*1 d@c1 = =14 * 4! * ' . d@c1 = =16 * 4! 44 14 .* d@c1 = =17 * 4! * ' . d@c1 = =1' * 4! 5! * .15 d@c1 = =1! * 4! 51 1' .5 d@c1 =1 =11 46 1 47 44 .1 d@c1 =1 =1* 46 1 5 47 .' d@c1 =1 =15 46 1 46 11 . d@c1 =1 =14 46 1 * ' .*1 d@c1 =1 =16 46 1 44 14 .1 d@c1 =1 =17 46 1 * ' .*1 d@c1 =1 =1' 46 1 5! * .! d@c1 =1 =1! 46 1 51 1' .1! d@c1 =11 =1* 47 44 5 47 .! d@c1 =11 =15 47 44 46 11 .1 d@c1 =11 =14 47 44 * ' .** d@c1 =11 =16 47 44 44 14 .* d@c1 =11 =17 47 44 * ' .** d@c1 =11 =1' 47 44 5! * . d@c1 =11 =1! 47 44 51 1' .1 d@c1 =1* =15 5 47 46 11 .' d@c1 =1* =14 5 47 * ' .16 d@c1 =1* =16 5 47 44 14 .7 d@c1 =1* =17 5 47 * ' .16 d@c1 =1* =1' 5 47 5! * .1 d@c1 =1* =1! 5 47 51 1' .11 d@c1 =15 =14 46 11 * ' .**
d@c1 =15 =16 46 11 44 14 .1 d@c1 =15 =17 46 11 * ' .** d@c1 =15 =1' 46 11 5! * .! d@c1 =15 =1! 46 11 51 1' .1! d@c1 =14 =16 * ' 44 14 .* d@c1 =14 =17 * ' * ' . d@c1 =14 =1' * ' 5! * .15 d@c1 =14 =1! * ' 51 1' .5 d@c1 =16 =17 44 14 * ' .* d@c1 =16 =1' 44 14 5! * .' d@c1 =16 =1! 44 14 51 1' .1' d@c1 =17 =1' * ' 5! * .15 d@c1 =17 =1! * ' 51 1' .5 d@c1 =1' =1! 5! * 51 1' .1
=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 *
d@c* =1 =* 4 55 1* 6 .4!
d@c* =1 =4 4 55 *1 57 .7! d@c* =1 =6 4 55 *! 5 .'6 d@c* =1 =7 4 55 5 *! .14 d@c* =1 =' 4 55 14 *! .66 d@c* =1 =! 4 55 44 .5! d@c* =1 = 4 55 *4 15 .' d@c* =1 =1 4 55 16 5 .6! d@c* =1 =11 4 55 7 5' .* d@c* =1 =1* 4 55 *7 44 .'5 d@c* =1 =15 4 55 *7 .5! d@c* =1 =14 4 55 *7 5 .'5 d@c* =1 =16 4 55 11 51 .4' d@c* =1 =17 4 55 ' 57 .*' d@c* =1 =1' 4 55 1* 7 .4! d@c* =1 =1! 4 55 *' *1 .'4 d@c* =1 =1 4 55 ! 14 .5* d@c* =1 =* 4 55 *' 15 .'5 d@c* =1 =*1 4 55 1 56 .7 d@c* =1 =** 4 55 ! 4 .55 d@c* =1 =*5 4 55 *5 6 .' d@c* =1 =*4 4 55 1 1 .6 d@c* =1 =*6 4 55 ** 4* .7 d@c* =1 =*7 4 55 *1 5* .7! d@c* =1 =*' 4 55 * 5! .55 d@c* =1 =*! 4 55 1* 44 .6 d@c* =1 =* 4 55 1* 55 .6 d@c* =* =5 1* 6 * 7 .'1 d@c* =* =4 1* 6 *1 57 .*' d@c* =* =6 1* 6 *! 5 .5 d@c* =* =7 1* 6 5 *! .6' d@c* =* =' 1* 6 14 *! .' d@c* =* =! 1* 6 44 .14 d@c* =* = 1* 6 *4 15 .55 d@c* =* =1 1* 6 16 5 .11 d@c* =* =11 1* 6 7 5' .5* d@c* =* =1* 1* 6 *7 44 .57 d@c* =* =15 1* 6 *7 .14 d@c* =* =14 1* 6 *7 5 .57 d@c* =* =16 1* 6 11 51 .4 d@c* =* =17 1* 6 ' 57 .*6
d@c* =* =1' 1* 6 1* 7 . d@c* =* =1! 1* 6 *' *1 .5! d@c* =* =1 1* 6 ! 14 .* d@c* =* =* 1* 6 *' 15 .5! d@c* =* =*1 1* 6 1 56 .! d@c* =* =** 1* 6 ! 4 .1 d@c* =* =*5 1* 6 *5 6 .51 d@c* =* =*4 1* 6 1 1 .! d@c* =* =*6 1* 6 ** 4* .* d@c* =* =*7 1* 6 *1 5* .*' d@c* =* =*' 1* 6 * 5! .7! d@c* =* =*! 1* 6 1* 44 . d@c* =* =* 1* 6 1* 55 . d@c* =5 =4 * 7 *1 57 .! d@c* =5 =6 * 7 *! 5 .!6 d@c* =5 =7 * 7 5 *! .1! d@c* =5 =' * 7 14 *! .'* d@c* =5 =! * 7 44 .7 d@c* =5 = * 7 *4 15 .!5 d@c* =5 =1 * 7 16 5 .'5 d@c* =5 =11 * 7 7 5' .47 d@c* =5 =1* * 7 *7 44 .!5 d@c* =5 =15 * 7 *7 .7 d@c* =5 =14 * 7 *7 5 .!4 d@c* =5 =16 * 7 11 51 .77 d@c* =5 =17 * 7 ' 57 .61 d@c* =5 =1' * 7 1* 7 .'1 d@c* =5 =1! * 7 *' *1 .!6 d@c* =5 =1 * 7 ! 14 .6! d@c* =5 =* * 7 *' 15 .!6 d@c* =5 =*1 * 7 1 56 .*' d@c* =5 =** * 7 ! 4 .67 d@c* =5 =*5 * 7 *5 6 .!1 d@c* =5 =*4 * 7 1 1 .*' d@c* =5 =*6 * 7 ** 4* .!1 d@c* =5 =*7 * 7 *1 5* .! d@c* =5 =*' * 7 * 5! . d@c* =5 =*! * 7 1* 44 .7! d@c* =5 =* * 7 1* 55 .7! d@c* =4 =6 *1 57 *! 5 .14
d@c* =4 =7 *1 57 5 *! .'6 d@c* =4 =' *1 57 14 *! .* d@c* =4 =! *1 57 44 .4 d@c* =4 = *1 57 *4 15 .' d@c* =4 =1 *1 57 16 5 .1' d@c* =4 =11 *1 57 7 5' .67 d@c* =4 =1* *1 57 *7 44 .11 d@c* =4 =15 *1 57 *7 .4 d@c* =4 =14 *1 57 *7 5 .11 d@c* =4 =16 *1 57 11 51 .51 d@c* =4 =17 *1 57 ' 57 .6 d@c* =4 =1' *1 57 1* 7 .*' d@c* =4 =1! *1 57 *' *1 .1* d@c* =4 =1 *1 57 ! 14 .44 d@c* =4 =* *1 57 *' 15 .1* d@c* =4 =*1 *1 57 1 56 .1 d@c* =4 =** *1 57 ! 4 .46 d@c* =4 =*5 *1 57 *5 6 .6 d@c* =4 =*4 *1 57 1 1 .!' d@c* =4 =*6 *1 57 ** 4* .* d@c* =4 =*7 *1 57 *1 5* . d@c* =4 =*' *1 57 * 5! .!5 d@c* =4 =*! *1 57 1* 44 .*' d@c* =4 =* *1 57 1* 55 .*' d@c* =6 =7 *! 5 5 *! .!1 d@c* =6 =' *! 5 14 *! .55 d@c* =6 =! *! 5 44 .61 d@c* =6 = *! 5 *4 15 .! d@c* =6 =1 *! 5 16 5 .5 d@c* =6 =11 *! 5 7 5' .76 d@c* =6 =1* *! 5 *7 44 .4 d@c* =6 =15 *! 5 *7 .61 d@c* =6 =14 *! 5 *7 5 .4 d@c* =6 =16 *! 5 11 51 .44 d@c* =6 =17 *! 5 ' 57 .7 d@c* =6 =1' *! 5 1* 7 .5 d@c* =6 =1! *! 5 *' *1 .* d@c* =6 =1 *! 5 ! 14 .66 d@c* =6 =* *! 5 *' 15 .* d@c* =6 =*1 *! 5 1 56 .5
d@c* =6 =** *! 5 ! 4 .66 d@c* =6 =*5 *! 5 *5 6 .1 d@c* =6 =*4 *! 5 1 1 . d@c* =6 =*6 *! 5 ** 4* .1* d@c* =6 =*7 *! 5 *1 5* .14 d@c* =6 =*' *! 5 * 5! .!7 d@c* =6 =*! *! 5 1* 44 .4 d@c* =6 =* *! 5 1* 55 .4 d@c* =7 =' 5 *! 14 *! .76 d@c* =7 =! 5 *! 44 .4 d@c* =7 = 5 *! *4 15 .'' d@c* =7 =1 5 *! 16 5 .77 d@c* =7 =11 5 *! 7 5' .55 d@c* =7 =1* 5 *! *7 44 .' d@c* =7 =15 5 *! *7 .6 d@c* =7 =14 5 *! *7 5 .' d@c* =7 =16 5 *! 11 51 .6' d@c* =7 =17 5 *! ' 57 .4 d@c* =7 =1' 5 *! 1* 7 .6! d@c* =7 =1! 5 *! *' *1 .! d@c* =7 =1 5 *! ! 14 .44 d@c* =7 =* 5 *! *' 15 .' d@c* =7 =*1 5 *! 1 56 .4 d@c* =7 =** 5 *! ! 4 .46 d@c* =7 =*5 5 *! *5 6 .'7 d@c* =7 =*4 5 *! 1 1 .41 d@c* =7 =*6 5 *! ** 4* .'6 d@c* =7 =*7 5 *! *1 5* .'6 d@c* =7 =*' 5 *! * 5! .1 d@c* =7 =*! 5 *! 1* 44 .6 d@c* =7 =* 5 *! 1* 55 .7 d@c* =' =! 14 *! 44 .** d@c* =' = 14 *! *4 15 .*7 d@c* =' =1 14 *! 16 5 .5 d@c* =' =11 14 *! 7 5' .4 d@c* =' =1* 14 *! *7 44 .5 d@c* =' =15 14 *! *7 .** d@c* =' =14 14 *! *7 5 .5 d@c* =' =16 14 *! 11 51 .1* d@c* =' =17 14 *! ' 57 .55 d@c* =' =1' 14 *! 1* 7 .!
d@c* =' =1! 14 *! *' *1 .5* d@c* =' =1 14 *! ! 14 .*' d@c* =' =* 14 *! *' 15 .51 d@c* =' =*1 14 *! 1 56 .!7 d@c* =' =** 14 *! ! 4 .*' d@c* =' =*5 14 *! *5 6 .*4 d@c* =' =*4 14 *! 1 1 .!* d@c* =' =*6 14 *! ** 4* .** d@c* =' =*7 14 *! *1 5* .* d@c* =' =*' 14 *! * 5! .'4 d@c* =' =*! 14 *! 1* 44 .! d@c* =' =* 14 *! 1* 55 .! d@c* =! = 44 *4 15 .46 d@c* =! =1 44 16 5 .*6 d@c* =! =11 44 7 5' .* d@c* =! =1* 44 *7 44 .4 d@c* =! =15 44 *7 . d@c* =! =14 44 *7 5 .4! d@c* =! =16 44 11 51 .1 d@c* =! =17 44 ' 57 .1* d@c* =! =1' 44 1* 7 .14 d@c* =! =1! 44 *' *1 .6 d@c* =! =1 44 ! 14 .7 d@c* =! =* 44 *' 15 .4 d@c* =! =*1 44 1 56 .' d@c* =! =** 44 ! 4 .7 d@c* =! =*5 44 *5 6 .44 d@c* =! =*4 44 1 1 .'5 d@c* =! =*6 44 ** 4* .4* d@c* =! =*7 44 *1 5* .4 d@c* =! =*' 44 * 5! .75 d@c* =! =*! 44 1* 44 .14 d@c* =! =* 44 1* 55 .14 d@c* = =1 *4 15 16 5 .*5 d@c* = =11 *4 15 7 5' .6 d@c* = =1* *4 15 *7 44 .4 d@c* = =15 *4 15 *7 .46 d@c* = =14 *4 15 *7 5 .4 d@c* = =16 *4 15 11 51 .5' d@c* = =17 *4 15 ' 57 .64 d@c* = =1' *4 15 1* 7 .55 d@c* = =1! *4 15 *' *1 .7
d@c* = =1 *4 15 ! 14 .6 d@c* = =* *4 15 *' 15 .7 d@c* = =*1 *4 15 1 56 . d@c* = =** *4 15 ! 4 .4 d@c* = =*5 *4 15 *5 6 .* d@c* = =*4 *4 15 1 1 .! d@c* = =*6 *4 15 ** 4* .4 d@c* = =*7 *4 15 *1 5* .' d@c* = =*' *4 15 * 5! .!5 d@c* = =*! *4 15 1* 44 .55 d@c* = =* *4 15 1* 55 .55 d@c* =1 =11 16 5 7 5' .45 d@c* =1 =1* 16 5 *7 44 .*' d@c* =1 =15 16 5 *7 .*6 d@c* =1 =14 16 5 *7 5 .*' d@c* =1 =16 16 5 11 51 .16 d@c* =1 =17 16 5 ' 57 .57 d@c* =1 =1' 16 5 1* 7 .11 d@c* =1 =1! 16 5 *' *1 .*! d@c* =1 =1 16 5 ! 14 .5 d@c* =1 =* 16 5 *' 15 .*! d@c* =1 =*1 16 5 1 56 .!' d@c* =1 =** 16 5 ! 4 .5 d@c* =1 =*5 16 5 *5 6 .*1 d@c* =1 =*4 16 5 1 1 .!5 d@c* =1 =*6 16 5 ** 4* .1 d@c* =1 =*7 16 5 *1 5* .1' d@c* =1 =*' 16 5 * 5! .'7 d@c* =1 =*! 16 5 1* 44 .11 d@c* =1 =* 16 5 1* 55 .11 d@c* =11 =1* 7 5' *7 44 .7* d@c* =11 =15 7 5' *7 .* d@c* =11 =14 7 5' *7 5 .7* d@c* =11 =16 7 5' 11 51 .* d@c* =11 =17 7 5' ' 57 .! d@c* =11 =1' 7 5' 1* 7 .5* d@c* =11 =1! 7 5' *' *1 .75 d@c* =11 =1 7 5' ! 14 .14 d@c* =11 =* 7 5' *' 15 .75 d@c* =11 =*1 7 5' 1 56 .'1 d@c* =11 =** 7 5' ! 4 .14 d@c* =11 =*5 7 5' *5 6 .6!
d@c* =11 =*4 7 5' 1 1 .75 d@c* =11 =*6 7 5' ** 4* .6' d@c* =11 =*7 7 5' *1 5* .66 d@c* =11 =*' 7 5' * 5! .6 d@c* =11 =*! 7 5' 1* 44 .55 d@c* =11 =* 7 5' 1* 55 .55 d@c* =1* =15 *7 44 *7 .4! d@c* =1* =14 *7 44 *7 5 . d@c* =1* =16 *7 44 11 51 .4 d@c* =1* =17 *7 44 ' 57 .6' d@c* =1* =1' *7 44 1* 7 .57 d@c* =1* =1! *7 44 *' *1 .* d@c* =1* =1 *7 44 ! 14 .6* d@c* =1* =* *7 44 *' 15 .* d@c* =1* =*1 *7 44 1 56 .* d@c* =1* =** *7 44 ! 4 .65 d@c* =1* =*5 *7 44 *5 6 .7 d@c* =1* =*4 *7 44 1 1 .! d@c* =1* =*6 *7 44 ** 4* .! d@c* =1* =*7 *7 44 *1 5* .11 d@c* =1* =*' *7 44 * 5! .!6 d@c* =1* =*! *7 44 1* 44 .5' d@c* =1* =* *7 44 1* 55 .5' d@c* =15 =14 *7 *7 5 .4! d@c* =15 =16 *7 11 51 .1 d@c* =15 =17 *7 ' 57 .1* d@c* =15 =1' *7 1* 7 .14 d@c* =15 =1! *7 *' *1 .6 d@c* =15 =1 *7 ! 14 .7 d@c* =15 =* *7 *' 15 .6 d@c* =15 =*1 *7 1 56 .' d@c* =15 =** *7 ! 4 .7 d@c* =15 =*5 *7 *5 6 .45 d@c* =15 =*4 *7 1 1 .'5 d@c* =15 =*6 *7 ** 4* .4* d@c* =15 =*7 *7 *1 5* .4 d@c* =15 =*' *7 * 5! .75 d@c* =15 =*! *7 1* 44 .14 d@c* =15 =* *7 1* 55 .14 d@c* =14 =16 *7 5 11 51 .4 d@c* =14 =17 *7 5 ' 57 .6! d@c* =14 =1' *7 5 1* 7 .57
d@c* =14 =1! *7 5 *' *1 .* d@c* =14 =1 *7 5 ! 14 .6* d@c* =14 =* *7 5 *' 15 .* d@c* =14 =*1 *7 5 1 56 .* d@c* =14 =** *7 5 ! 4 .65 d@c* =14 =*5 *7 5 *5 6 .7 d@c* =14 =*4 *7 5 1 1 .! d@c* =14 =*6 *7 5 ** 4* .! d@c* =14 =*7 *7 5 *1 5* .11 d@c* =14 =*' *7 5 * 5! .!7 d@c* =14 =*! *7 5 1* 44 .5' d@c* =14 =* *7 5 1* 55 .5' d@c* =16 =17 11 51 ' 57 .** d@c* =16 =1' 11 51 1* 7 .4 d@c* =16 =1! 11 51 *' *1 .4* d@c* =16 =1 11 51 ! 14 .16 d@c* =16 =* 11 51 *' 15 .4* d@c* =16 =*1 11 51 1 56 .!5 d@c* =16 =** 11 51 ! 4 .17 d@c* =16 =*5 11 51 *5 6 .56 d@c* =16 =*4 11 51 1 1 .'' d@c* =16 =*6 11 51 ** 4* .55 d@c* =16 =*7 11 51 *1 5* .51 d@c* =16 =*' 11 51 * 5! .7 d@c* =16 =*! 11 51 1* 44 .4 d@c* =16 =* 11 51 1* 55 .4 d@c* =17 =1' ' 57 1* 7 .*6 d@c* =17 =1! ' 57 *' *1 .6! d@c* =17 =1 ' 57 ! 14 .7 d@c* =17 =* ' 57 *' 15 .6! d@c* =17 =*1 ' 57 1 56 .'6 d@c* =17 =** ' 57 ! 4 .' d@c* =17 =*5 ' 57 *5 6 .65 d@c* =17 =*4 ' 57 1 1 .7' d@c* =17 =*6 ' 57 ** 4* .6* d@c* =17 =*7 ' 57 *1 5* .6 d@c* =17 =*' ' 57 * 5! .66 d@c* =17 =*! ' 57 1* 44 .*7 d@c* =17 =* ' 57 1* 55 .*7 d@c* =1' =1! 1* 7 *' *1 .5! d@c* =1' =1 1* 7 ! 14 .* d@c* =1' =* 1* 7 *' 15 .5!
d@c* =1' =*1 1* 7 1 56 .! d@c* =1' =** 1* 7 ! 4 .1 d@c* =1' =*5 1* 7 *5 6 .51 d@c* =1' =*4 1* 7 1 1 .! d@c* =1' =*6 1* 7 ** 4* .* d@c* =1' =*7 1* 7 *1 5* .*' d@c* =1' =*' 1* 7 * 5! .7! d@c* =1' =*! 1* 7 1* 44 . d@c* =1' =* 1* 7 1* 55 . d@c* =1! =1 *' *1 ! 14 .64 d@c* =1! =* *' *1 *' 15 . d@c* =1! =*1 *' *1 1 56 .* d@c* =1! =** *' *1 ! 4 .64 d@c* =1! =*5 *' *1 *5 6 .! d@c* =1! =*4 *' *1 1 1 . d@c* =1! =*6 *' *1 ** 4* .1 d@c* =1! =*7 *' *1 *1 5* .1* d@c* =1! =*' *' *1 * 5! .!6 d@c* =1! =*! *' *1 1* 44 .5! d@c* =1! =* *' *1 1* 55 .5! d@c* =1 =* ! 14 *' 15 .64 d@c* =1 =*1 ! 14 1 56 .'4 d@c* =1 =** ! 14 ! 4 . d@c* =1 =*5 ! 14 *5 6 .4! d@c* =1 =*4 ! 14 1 1 .'1 d@c* =1 =*6 ! 14 ** 4* .47 d@c* =1 =*7 ! 14 *1 5* .44 d@c* =1 =*' ! 14 * 5! .6' d@c* =1 =*! ! 14 1* 44 .1 d@c* =1 =* ! 14 1* 55 .* d@c* =* =*1 *' 15 1 56 .1 d@c* =* =** *' 15 ! 4 .64 d@c* =* =*5 *' 15 *5 6 .! d@c* =* =*4 *' 15 1 1 . d@c* =* =*6 *' 15 ** 4* .1 d@c* =* =*7 *' 15 *1 5* .1* d@c* =* =*' *' 15 * 5! .!6 d@c* =* =*! *' 15 1* 44 .5! d@c* =* =* *' 15 1* 55 .5! d@c* =*1 =** 1 56 ! 4 .'' d@c* =*1 =*5 1 56 *5 6 .1 d@c* =*1 =*4 1 56 1 1 .
d@c* =*1 =*6 1 56 ** 4* .1 d@c* =*1 =*7 1 56 *1 5* .1 d@c* =*1 =*' 1 56 * 5! .55 d@c* =*1 =*! 1 56 1* 44 .!4 d@c* =*1 =* 1 56 1* 55 .!4 d@c* =** =*5 ! 4 *5 6 .4! d@c* =** =*4 ! 4 1 1 .' d@c* =** =*6 ! 4 ** 4* .4' d@c* =** =*7 ! 4 *1 5* .46 d@c* =** =*' ! 4 * 5! .7 d@c* =** =*! ! 4 1* 44 .* d@c* =** =* ! 4 1* 55 .* d@c* =*5 =*4 *5 6 1 1 .!! d@c* =*5 =*6 *5 6 ** 4* .* d@c* =*5 =*7 *5 6 *1 5* .6 d@c* =*5 =*' *5 6 * 5! .!4 d@c* =*5 =*! *5 6 1* 44 .51 d@c* =*5 =* *5 6 1* 55 .51 d@c* =*4 =*6 1 1 ** 4* .!! d@c* =*4 =*7 1 1 *1 5* .!' d@c* =*4 =*' 1 1 * 5! .*6 d@c* =*4 =*! 1 1 1* 44 .' d@c* =*4 =* 1 1 1* 55 .' d@c* =*6 =*7 ** 4* *1 5* .* d@c* =*6 =*' ** 4* * 5! .!5 d@c* =*6 =*! ** 4* 1* 44 .* d@c* =*6 =* ** 4* 1* 55 .* d@c* =*7 =*' *1 5* * 5! .!* d@c* =*7 =*! *1 5* 1* 44 .*' d@c* =*7 =* *1 5* 1* 55 .*' d@c* =*' =*! * 5! 1* 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 c1 =1 c* = 47 1 *4 15 .51 d c1 =1 c* =1 47 1 16 5 .6 d c1 =1 c* =11 47 1 7 5' .'7 d c1 =1 c* =1* 47 1 *7 44 .*! d c1 =1 c* =15 47 1 *7 .7' d c1 =1 c* =14 47 1 *7 5 .*! d c1 =1 c* =16 47 1 11 51 .71
d c1 =1 c* =17 47 1 ' 57 .'5 d c1 =1 c* =1' 47 1 1* 7 .6! d c1 =1 c* =1! 47 1 *' *1 .*7 d c1 =1 c* =1 47 1 ! 14 .' d c1 =1 c* =* 47 1 *' 15 .*7 d c1 =1 c* =*1 47 1 1 56 .6 d c1 =1 c* =** 47 1 ! 4 .' d c1 =1 c* =*5 47 1 *5 6 .55 d c1 =1 c* =*4 47 1 1 1 .4 d c1 =1 c* =*6 47 1 ** 4* .56 d c1 =1 c* =*7 47 1 *1 5* .5' d c1 =1 c* =*' 47 1 * 5! .1 d c1 =1 c* =*! 47 1 1* 44 .6! d c1 =1 c* =* 47 1 1* 55 .6! d c1 =* c* =1 51 41 4 55 .'' d c1 =* c* =* 51 41 1* 6 .45 d c1 =* c* =5 51 41 * 7 .!7 d c1 =* c* =4 51 41 *1 57 .1 d c1 =* c* =6 51 41 *! 5 .6 d c1 =* c* =7 51 41 5 *! .!* d c1 =* c* =' 51 41 14 *! .5! d c1 =* c* =! 51 41 44 .66 d c1 =* c* = 51 41 *4 15 .15 d c1 =* c* =1 51 41 16 5 .56 d c1 =* c* =11 51 41 7 5' .7' d c1 =* c* =1* 51 41 *7 44 . d c1 =* c* =15 51 41 *7 .66 d c1 =* c* =14 51 41 *7 5 . d c1 =* c* =16 51 41 11 51 .4' d c1 =* c* =17 51 41 ' 57 .75 d c1 =* c* =1' 51 41 1* 7 .45 d c1 =* c* =1! 51 41 *' *1 .' d c1 =* c* =1 51 41 ! 14 .6! d c1 =* c* =* 51 41 *' 15 .' d c1 =* c* =*1 51 41 1 56 .4 d c1 =* c* =** 51 41 ! 4 .6 d c1 =* c* =*5 51 41 *5 6 .16 d c1 =* c* =*4 51 41 1 1 .1 d c1 =* c* =*6 51 41 ** 4* .1' d c1 =* c* =*7 51 41 *1 5* .1 d c1 =* c* =*' 51 41 * 5! .!! d c1 =* c* =*! 51 41 1* 44 .44
d c1 =* c* =* 51 41 1* 55 .44 d c1 =5 c* =1 47 * 4 55 .!4 d c1 =* c* =* 47 * 1* 6 .6! d c1 =* c* =5 47 * * 7 .1 d c1 =* c* =4 47 * *1 57 .5' d c1 =* c* =6 47 * *! 5 .*4 d c1 =* c* =7 47 * 5 *! .!' d c1 =* c* =' 47 * 14 *! .65 d c1 =* c* =! 47 * 44 .7' d c1 =* c* = 47 * *4 15 .51 d c1 =* c* =1 47 * 16 5 .61 d c1 =* c* =11 47 * 7 5' .'7 d c1 =* c* =1* 47 * *7 44 .*! d c1 =* c* =15 47 * *7 .7' d c1 =* c* =14 47 * *7 5 .*! d c1 =* c* =16 47 * 11 51 .71 d c1 =* c* =17 47 * ' 57 .'5 d c1 =* c* =1' 47 * 1* 7 .6! d c1 =* c* =1! 47 * *' *1 .*7 d c1 =* c* =1 47 * ! 14 .' d c1 =* c* =* 47 * *' 15 .*7 d c1 =* c* =*1 47 * 1 56 .6 d c1 =* c* =** 47 * ! 4 .' d c1 =* c* =*5 47 * *5 6 .55 d c1 =* c* =*4 47 * 1 1 .4 d c1 =* c* =*6 47 * ** 4* .56 d c1 =* c* =*7 47 * *1 5* .5' d c1 =* c* =*' 47 * * 5! .1 d c1 =* c* =*! 47 * 1* 44 .6! d c1 =* c* =* 47 * 1* 55 .6! d c1 =4 c* =1 44 11 4 55 .!* d c1 =4 c* =* 44 11 1* 6 .6' d c1 =4 c* =5 44 11 * 7 .1 d c1 =4 c* =4 44 11 *1 57 .56 d c1 =4 c* =6 44 11 *! 5 .** d c1 =4 c* =7 44 11 5 *! .!7 d c1 =4 c* =' 44 11 14 *! .61 d c1 =4 c* =! 44 11 44 .76 d c1 =4 c* = 44 11 *4 15 .* d c1 =4 c* =1 44 11 16 5 .4 d c1 =4 c* =11 44 11 7 5' .'6 d c1 =4 c* =1* 44 11 *7 44 .*6
d c1 =4 c* =15 44 11 *7 .77 d c1 =4 c* =14 44 11 *7 5 .*7 d c1 =4 c* =16 44 11 11 51 .6 d c1 =4 c* =17 44 11 ' 57 .'* d c1 =4 c* =1' 44 11 1* 7 .6' d c1 =4 c* =1! 44 11 *' *1 .*4 d c1 =4 c* =1 44 11 ! 14 .7 d c1 =4 c* =* 44 11 *' 15 .*4 d c1 =4 c* =*1 44 11 1 56 .4 d c1 =4 c* =** 44 11 ! 4 .7! d c1 =4 c* =*5 44 11 *5 6 .51 d c1 =4 c* =*4 44 11 1 1 .4 d c1 =4 c* =*6 44 11 ** 4* .55 d c1 =4 c* =*7 44 11 *1 5* .56 d c1 =4 c* =*' 44 11 * 5! . d c1 =4 c* =*! 44 11 1* 44 .6' d c1 =4 c* =* 44 11 1* 55 .6' d c1 =6 c* =1 41 *4 4 55 .!* d c1 =6 c* =* 41 *4 1* 6 .64 d c1 =6 c* =5 41 *4 * 7 .! d c1 =6 c* =4 41 *4 *1 57 .5* d c1 =6 c* =6 41 *4 *! 5 .1 d c1 =6 c* =7 41 *4 5 *! .!7 d c1 =6 c* =' 41 *4 14 *! .4 d c1 =6 c* =! 41 *4 44 .74 d c1 =6 c* = 41 *4 *4 15 .*7 d c1 =6 c* =1 41 *4 16 5 .47 d c1 =6 c* =11 41 *4 7 5' .'4 d c1 =6 c* =1* 41 *4 *7 44 .** d c1 =6 c* =15 41 *4 *7 .74 d c1 =6 c* =14 41 *4 *7 5 .** d c1 =6 c* =16 41 *4 11 51 .6! d c1 =6 c* =17 41 *4 ' 57 .'1 d c1 =6 c* =1' 41 *4 1* 7 .64 d c1 =6 c* =1! 41 *4 *' *1 .*1 d c1 =6 c* =1 41 *4 ! 14 .7' d c1 =6 c* =* 41 *4 *' 15 .* d c1 =6 c* =*1 41 *4 1 56 .6 d c1 =6 c* =** 41 *4 ! 4 .7' d c1 =6 c* =*5 41 *4 *5 6 .*! d c1 =6 c* =*4 41 *4 1 1 .5 d c1 =6 c* =*6 41 *4 ** 4* .5
d c1 =6 c* =*7 41 *4 *1 5* .5* d c1 =6 c* =*' 41 *4 * 5! . d c1 =6 c* =*! 41 *4 1* 44 .64 d c1 =6 c* =* 41 *4 1* 55 .66 d c1 =7 c* =1 46 ! 4 55 .!5 d c1 =7 c* =* 46 ! 1* 6 .6! d c1 =7 c* =5 46 ! * 7 .1 d c1 =7 c* =4 46 ! *1 57 .57 d c1 =7 c* =6 46 ! *! 5 .*5 d c1 =7 c* =7 46 ! 5 *! .!7 d c1 =7 c* =' 46 ! 14 *! .6* d c1 =7 c* =! 46 ! 44 .77 d c1 =7 c* = 46 ! *4 15 .5 d c1 =7 c* =1 46 ! 16 5 .4 d c1 =7 c* =11 46 ! 7 5' .'7 d c1 =7 c* =1* 46 ! *7 44 .*' d c1 =7 c* =15 46 ! *7 .77 d c1 =7 c* =14 46 ! *7 5 .*' d c1 =7 c* =16 46 ! 11 51 .7 d c1 =7 c* =17 46 ! ' 57 .'* d c1 =7 c* =1' 46 ! 1* 7 .6! d c1 =7 c* =1! 46 ! *' *1 .*6 d c1 =7 c* =1 46 ! ! 14 .7 d c1 =7 c* =* 46 ! *' 15 .*6 d c1 =7 c* =*1 46 ! 1 56 .4 d c1 =7 c* =** 46 ! ! 4 .7 d c1 =7 c* =*5 46 ! *5 6 .5* d c1 =7 c* =*4 46 ! 1 1 .4 d c1 =7 c* =*6 46 ! ** 4* .54 d c1 =7 c* =*7 46 ! *1 5* .57 d c1 =7 c* =*' 46 ! * 5! . d c1 =7 c* =*! 46 ! 1* 44 .6' d c1 =7 c* =* 46 ! 1* 55 .6' d c1 =' c* =1 57 1' 4 55 .' d c1 =' c* =* 57 1' 1* 6 .4 d c1 =' c* =5 57 1' * 7 .!! d c1 =' c* =4 57 1' *1 57 .*7 d c1 =' c* =6 57 1' *! 5 .1* d c1 =' c* =7 57 1' 5 *! .!4 d c1 =' c* =' 57 1' 14 *! .44 d c1 =' c* =! 57 1' 44 .6 d c1 =' c* = 57 1' *4 15 .*
d c1 =' c* =1 57 1' 16 5 .41 d c1 =' c* =11 57 1' 7 5' .'1 d c1 =' c* =1* 57 1' *7 44 .17 d c1 =' c* =15 57 1' *7 .7 d c1 =' c* =14 57 1' *7 5 .17 d c1 =' c* =16 57 1' 11 51 .65 d c1 =' c* =17 57 1' ' 57 .7' d c1 =' c* =1' 57 1' 1* 7 .6 d c1 =' c* =1! 57 1' *' *1 .14 d c1 =' c* =1 57 1' ! 14 .75 d c1 =' c* =* 57 1' *' 15 .14 d c1 =' c* =*1 57 1' 1 56 .4 d c1 =' c* =** 57 1' ! 4 .75 d c1 =' c* =*5 57 1' *5 6 .** d c1 =' c* =*4 57 1' 1 1 .* d c1 =' c* =*6 57 1' ** 4* .*4 d c1 =' c* =*7 57 1' *1 5* .*7 d c1 =' c* =*' 57 1' * 5! .! d c1 =' c* =*! 57 1' 1* 44 .6 d c1 =' c* =* 57 1' 1* 55 .6 d c1 =! c* =1 46 *! 4 55 .!4 d c1 =! c* =* 46 *! 1* 6 .6' d c1 =! c* =5 46 *! * 7 . d c1 =! c* =4 46 *! *1 57 .57 d c1 =! c* =6 46 *! *! 5 .*5 d c1 =! c* =7 46 *! 5 *! .!! d c1 =! c* =' 46 *! 14 *! .65 d c1 =! c* =! 46 *! 44 .77 d c1 =! c* = 46 *! *4 15 .5 d c1 =! c* =1 46 *! 16 5 .6 d c1 =! c* =11 46 *! 7 5' .'7 d c1 =! c* =1* 46 *! *7 44 .*' d c1 =! c* =15 46 *! *7 .7' d c1 =! c* =14 46 *! *7 5 .*' d c1 =! c* =16 46 *! 11 51 .71 d c1 =! c* =17 46 *! ' 57 .'5 d c1 =! c* =1' 46 *! 1* 7 .6' d c1 =! c* =1! 46 *! *' *1 .*6 d c1 =! c* =1 46 *! ! 14 .7 d c1 =! c* =* 46 *! *' 15 .*6 d c1 =! c* =*1 46 *! 1 56 .6 d c1 =! c* =** 46 *! ! 4 .'
d c1 =! c* =*5 46 *! *5 6 .5* d c1 =! c* =*4 46 *! 1 1 .4 d c1 =! c* =*6 46 *! ** 4* .54 d c1 =! c* =*7 46 *! *1 5* .57 d c1 =! c* =*' 46 *! * 5! .1 d c1 =! c* =*! 46 *! 1* 44 .6! d c1 =! c* =* 46 *! 1* 55 .6! d c1 = c* =1 * 4! 4 55 .'6 d c1 = c* =* * 4! 1* 6 .41 d c1 = c* =5 * 4! * 7 .!6 d c1 = c* =4 * 4! *1 57 .17 d c1 = c* =6 * 4! *! 5 .* d c1 = c* =7 * 4! 5 *! .!1 d c1 = c* =' * 4! 14 *! .56 d c1 = c* =! * 4! 44 .65 d c1 = c* = * 4! *4 15 . d c1 = c* =1 * 4! 16 5 .5* d c1 = c* =11 * 4! 7 5' .76 d c1 = c* =1* * 4! *7 44 .6 d c1 = c* =15 * 4! *7 .6* d c1 = c* =14 * 4! *7 5 .6 d c1 = c* =16 * 4! 11 51 .46 d c1 = c* =17 * 4! ' 57 .71 d c1 = c* =1' * 4! 1* 7 .41 d c1 = c* =1! * 4! *' *1 .4 d c1 = c* =1 * 4! ! 14 .67 d c1 = c* =* * 4! *' 15 .4 d c1 = c* =*1 * 4! 1 56 .5 d c1 = c* =** * 4! ! 4 .6' d c1 = c* =*5 * 4! *5 6 .1* d c1 = c* =*4 * 4! 1 1 . d c1 = c* =*6 * 4! ** 4* .14 d c1 = c* =*7 * 4! *1 5* .17 d c1 = c* =*' * 4! * 5! .!' d c1 = c* =*! * 4! 1* 44 .41 d c1 = c* =* * 4! 1* 55 .41 d c1 =1 c* =1 46 1 4 55 .!5 d c1 =1 c* =* 46 1 1* 6 .6' d c1 =1 c* =5 46 1 * 7 . d c1 =1 c* =4 46 1 *1 57 .57 d c1 =1 c* =6 46 1 *! 5 .*5 d c1 =1 c* =7 46 1 5 *! .!'
d c1 =1 c* =' 46 1 14 *! .6* d c1 =1 c* =! 46 1 44 .77 d c1 =1 c* = 46 1 *4 15 .5 d c1 =1 c* =1 46 1 16 5 .6 d c1 =1 c* =11 46 1 7 5' .'7 d c1 =1 c* =1* 46 1 *7 44 .*' d c1 =1 c* =15 46 1 *7 .77 d c1 =1 c* =14 46 1 *7 5 .*' d c1 =1 c* =16 46 1 11 51 .7 d c1 =1 c* =17 46 1 ' 57 .'5 d c1 =1 c* =1' 46 1 1* 7 .6' d c1 =1 c* =1! 46 1 *' *1 .*6 d c1 =1 c* =1 46 1 ! 14 .' d c1 =1 c* =* 46 1 *' 15 .*6 d c1 =1 c* =*1 46 1 1 56 .6 d c1 =1 c* =** 46 1 ! 4 .7 d c1 =1 c* =*5 46 1 *5 6 .5* d c1 =1 c* =*4 46 1 1 1 .4 d c1 =1 c* =*6 46 1 ** 4* .54 d c1 =1 c* =*7 46 1 *1 5* .57 d c1 =1 c* =*' 46 1 * 5! .1 d c1 =1 c* =*! 46 1 1* 44 .6' d c1 =1 c* =* 46 1 1* 55 .6! d c1 =11 c* =1 47 44 4 55 .!4 d c1 =11 c* =* 47 44 1* 6 .6! d c1 =11 c* =5 47 44 * 7 . d c1 =11 c* =4 47 44 *1 57 .5' d c1 =11 c* =6 47 44 *! 5 .*4 d c1 =11 c* =7 47 44 5 *! .!' d c1 =11 c* =' 47 44 14 *! .65 d c1 =11 c* =! 47 44 44 .7' d c1 =11 c* = 47 44 *4 15 .51 d c1 =11 c* =1 47 44 16 5 .61 d c1 =11 c* =11 47 44 7 5' .'' d c1 =11 c* =1* 47 44 *7 44 .*! d c1 =11 c* =15 47 44 *7 .7' d c1 =11 c* =14 47 44 *7 5 .*! d c1 =11 c* =16 47 44 11 51 .71 d c1 =11 c* =17 47 44 ' 57 .'5 d c1 =11 c* =1' 47 44 1* 7 .6! d c1 =11 c* =1! 47 44 *' *1 .*7 d c1 =11 c* =1 47 44 ! 14 .'
d c1 =11 c* =* 47 44 *' 15 .*7 d c1 =11 c* =*1 47 44 1 56 .7 d c1 =11 c* =** 47 44 ! 4 .' d c1 =11 c* =*5 47 44 *5 6 .55 d c1 =11 c* =*4 47 44 1 1 .4 d c1 =11 c* =*6 47 44 ** 4* .56 d c1 =11 c* =*7 47 44 *1 5* .5' d c1 =11 c* =*' 47 44 * 5! .* d c1 =11 c* =*! 47 44 1* 44 .6 d c1 =11 c* =* 47 44 1* 55 .6! d c1 =1* c* =1 5 47 4 55 .!1 d c1 =1* c* =* 5 47 1* 6 .6* d c1 =1* c* =5 5 47 * 7 .! d c1 =1* c* =4 5 47 *1 57 .5 d c1 =1* c* =6 5 47 *! 5 .17 d c1 =1* c* =7 5 47 5 *! .!6 d c1 =1* c* =' 5 47 14 *! .4' d c1 =1* c* =! 5 47 44 .7* d c1 =1* c* = 5 47 *4 15 .*4 d c1 =1* c* =1 5 47 16 5 .44 d c1 =1* c* =11 5 47 7 5' .'5 d c1 =1* c* =1* 5 47 *7 44 .* d c1 =1* c* =15 5 47 *7 .7* d c1 =1* c* =14 5 47 *7 5 .* d c1 =1* c* =16 5 47 11 51 .67 d c1 =1* c* =17 5 47 ' 57 .7 d c1 =1* c* =1' 5 47 1* 7 .6* d c1 =1* c* =1! 5 47 *' *1 .1! d c1 =1* c* =1 5 47 ! 14 .76 d c1 =1* c* =* 5 47 *' 15 .1! d c1 =1* c* =*1 5 47 1 56 .6 d c1 =1* c* =** 5 47 ! 4 .77 d c1 =1* c* =*5 5 47 *5 6 .*7 d c1 =1* c* =*4 5 47 1 1 .5 d c1 =1* c* =*6 5 47 ** 4* .*! d c1 =1* c* =*7 5 47 *1 5* .5 d c1 =1* c* =*' 5 47 * 5! . d c1 =1* c* =*! 5 47 1* 44 .65 d c1 =1* c* =* 5 47 1* 55 .65 d c1 =1* c* =1 5 47 4 55 .!1 d c1 =1* c* =* 5 47 1* 6 .6* d c1 =1* c* =5 5 47 * 7 .!
d c1 =1* c* =4 5 47 *1 57 .5 d c1 =1* c* =6 5 47 *! 5 .17 d c1 =1* c* =7 5 47 5 *! .!6 d c1 =1* c* =' 5 47 14 *! .4' d c1 =1* c* =! 5 47 44 .7* d c1 =1* c* = 5 47 *4 15 .*4 d c1 =1* c* =1 5 47 16 5 .44 d c1 =1* c* =11 5 47 7 5' .'5 d c1 =1* c* =1* 5 47 *7 44 .* d c1 =1* c* =15 5 47 *7 .7* d c1 =1* c* =14 5 47 *7 5 .* d c1 =1* c* =16 5 47 11 51 .67 d c1 =1* c* =17 5 47 ' 57 .7 d c1 =1* c* =1' 5 47 1* 7 .6* d c1 =1* c* =1! 5 47 *' *1 .1! d c1 =1* c* =1 5 47 ! 14 .76 d c1 =1* c* =* 5 47 *' 15 .1! d c1 =1* c* =*1 5 47 1 56 .6 d c1 =1* c* =** 5 47 ! 4 .77 d c1 =1* c* =*5 5 47 *5 6 .*7 d c1 =1* c* =*4 5 47 1 1 .5 d c1 =1* c* =*6 5 47 ** 4* .*! d c1 =1* c* =*7 5 47 *1 5* .5 d c1 =1* c* =*' 5 47 * 5! . d c1 =1* c* =*! 5 47 1* 44 .65 d c1 =1* c* =* 5 47 1* 55 .65 d c1 =14 c* =1 * ' 4 55 .'4 d c1 =14 c* =* * ' 1* 6 .41 d c1 =14 c* =5 * ' * 7 .!' d c1 =14 c* =4 * ' *1 57 .17 d c1 =14 c* =6 * ' *! 5 .* d c1 =14 c* =7 * ' 5 *! .! d c1 =14 c* =' * ' 14 *! .54 d c1 =14 c* =! * ' 44 .6* d c1 =14 c* = * ' *4 15 . d c1 =14 c* =1 * ' 16 5 .51 d c1 =14 c* =11 * ' 7 5' .74 d c1 =14 c* =1* * ' *7 44 .6 d c1 =14 c* =15 * ' *7 .6* d c1 =14 c* =14 * ' *7 5 .6 d c1 =14 c* =16 * ' 11 51 .44 d c1 =14 c* =17 * ' ' 57 .7
d c1 =14 c* =1' * ' 1* 7 .41 d c1 =14 c* =1! * ' *' *1 .4 d c1 =14 c* =1 * ' ! 14 .67 d c1 =14 c* =* * ' *' 15 .4 d c1 =14 c* =*1 * ' 1 56 .1 d c1 =14 c* =** * ' ! 4 .67 d c1 =14 c* =*5 * ' *5 6 .11 d c1 =14 c* =*4 * ' 1 1 .1 d c1 =14 c* =*6 * ' ** 4* .14 d c1 =14 c* =*7 * ' *1 5* .17 d c1 =14 c* =*' * ' * 5! .!6 d c1 =14 c* =*! * ' 1* 44 .41 d c1 =14 c* =* * ' 1* 55 .41 d c1 =16 c* =1 44 14 4 55 .!5 d c1 =16 c* =* 44 14 1* 6 .6' d c1 =16 c* =5 44 14 * 7 .1 d c1 =16 c* =4 44 14 *1 57 .56 d c1 =16 c* =6 44 14 *! 5 .** d c1 =16 c* =7 44 14 5 *! .!' d c1 =16 c* =' 44 14 14 *! .61 d c1 =16 c* =! 44 14 44 .76 d c1 =16 c* = 44 14 *4 15 .* d c1 =16 c* =1 44 14 16 5 .4 d c1 =16 c* =11 44 14 7 5' .'6 d c1 =16 c* =1* 44 14 *7 44 .*7 d c1 =16 c* =15 44 14 *7 .77 d c1 =16 c* =14 44 14 *7 5 .*7 d c1 =16 c* =16 44 14 11 51 .7 d c1 =16 c* =17 44 14 ' 57 .'* d c1 =16 c* =1' 44 14 1* 7 .6' d c1 =16 c* =1! 44 14 *' *1 .*4 d c1 =16 c* =1 44 14 ! 14 .7 d c1 =16 c* =* 44 14 *' 15 .*4 d c1 =16 c* =*1 44 14 1 56 .6 d c1 =16 c* =** 44 14 ! 4 .7 d c1 =16 c* =*5 44 14 *5 6 .51 d c1 =16 c* =*4 44 14 1 1 .4 d c1 =16 c* =*6 44 14 ** 4* .55 d c1 =16 c* =*7 44 14 *1 5* .56 d c1 =16 c* =*' 44 14 * 5! . d c1 =16 c* =*! 44 14 1* 44 .6' d c1 =16 c* =* 44 14 1* 55 .6'
d c1 =17 c* =1 * ' 4 55 .'4 d c1 =17 c* =* * ' 1* 6 .41 d c1 =17 c* =5 * ' * 7 .!' d c1 =17 c* =4 * ' *1 57 .17 d c1 =17 c* =6 * ' *! 5 .* d c1 =17 c* =7 * ' 5 *! .! d c1 =17 c* =' * ' 14 *! .54 d c1 =17 c* =! * ' 44 .6* d c1 =17 c* = * ' *4 15 . d c1 =17 c* =1 * ' 16 5 .51 d c1 =17 c* =11 * ' 7 5' .74 d c1 =17 c* =1* * ' *7 44 .6 d c1 =17 c* =15 * ' *7 .6* d c1 =17 c* =14 * ' *7 5 .6 d c1 =17 c* =16 * ' 11 51 .44 d c1 =17 c* =17 * ' ' 57 .7 d c1 =17 c* =1' * ' 1* 7 .41 d c1 =17 c* =1! * ' *' *1 .4 d c1 =17 c* =1 * ' ! 14 .67 d c1 =17 c* =* * ' *' 15 .4 d c1 =17 c* =*1 * ' 1 56 .1 d c1 =17 c* =** * ' ! 4 .67 d c1 =17 c* =*5 * ' *5 6 .11 d c1 =17 c* =*4 * ' 1 1 .1 d c1 =17 c* =*6 * ' ** 4* .14 d c1 =17 c* =*7 * ' *1 5* .17 d c1 =17 c* =*' * ' * 5! .!6 d c1 =17 c* =*! * ' 1* 44 .41 d c1 =17 c* =* * ' 1* 55 .41 d c1 =1' c* =1 5! * 4 55 .! d c1 =1' c* =* 5! * 1* 6 .61 d c1 =1' c* =5 5! * * 7 .! d c1 =1' c* =4 5! * *1 57 .* d c1 =1' c* =6 5! * *! 5 .16 d c1 =1' c* =7 5! * 5 *! .!6 d c1 =1' c* =' 5! * 14 *! .47 d c1 =1' c* =! 5! * 44 .71 d c1 =1' c* = 5! * *4 15 .*5 d c1 =1' c* =1 5! * 16 5 .45 d c1 =1' c* =11 5! * 7 5' .'* d c1 =1' c* =1* 5! * *7 44 .1 d c1 =1' c* =15 5! * *7 .7*
d c1 =1' c* =14 5! * *7 5 .1 d c1 =1' c* =16 5! * 11 51 .66 d c1 =1' c* =17 5! * ' 57 .7! d c1 =1' c* =1' 5! * 1* 7 .61 d c1 =1' c* =1! 5! * *' *1 .1' d c1 =1' c* =1 5! * ! 14 .76 d c1 =1' c* =* 5! * *' 15 .1' d c1 =1' c* =*1 5! * 1 56 .4 d c1 =1' c* =** 5! * ! 4 .76 d c1 =1' c* =*5 5! * *5 6 .*4 d c1 =1' c* =*4 5! * 1 1 .5 d c1 =1' c* =*6 5! * ** 4* .*' d c1 =1' c* =*7 5! * *1 5* .* d c1 =1' c* =*' 5! * * 5! .! d c1 =1' c* =*! 5! * 1* 44 .6* d c1 =1' c* =* 5! * 1* 55 .6* d c1 =1! c* =1 51 1' 4 55 .'7 d c1 =1! c* =* 51 1' 1* 6 .44 d c1 =1! c* =5 51 1' * 7 .!' d c1 =1! c* =4 51 1' *1 57 .1 d c1 =1! c* =6 51 1' *! 5 .6 d c1 =1! c* =7 51 1' 5 *! .!* d c1 =1! c* =' 51 1' 14 *! .5! d c1 =1! c* =! 51 1' 44 .64 d c1 =1! c* = 51 1' *4 15 .15 d c1 =1! c* =1 51 1' 16 5 .54 d c1 =1! c* =11 51 1' 7 5' .7' d c1 =1! c* =1* 51 1' *7 44 . d c1 =1! c* =15 51 1' *7 .66 d c1 =1! c* =14 51 1' *7 5 . d c1 =1! c* =16 51 1' 11 51 .4' d c1 =1! c* =17 51 1' ' 57 .75 d c1 =1! c* =1' 51 1' 1* 7 .44 d c1 =1! c* =1! 51 1' *' *1 .' d c1 =1! c* =1 51 1' ! 14 .6 d c1 =1! c* =* 51 1' *' 15 .' d c1 =1! c* =*1 51 1' 1 56 .5 d c1 =1! c* =** 51 1' ! 4 .6! d c1 =1! c* =*5 51 1' *5 6 .16 d c1 =1! c* =*4 51 1' 1 1 .1 d c1 =1! c* =*6 51 1' ** 4* .1' d c1 =1! c* =*7 51 1' *1 5* .1
d c1 =1! c* =*' 51 1' * 5! .!'
d c1 =1! c* =*! 51 1' 1* 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"
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 1 16 7 5' 47 * 1* 56 *7 44 11 *1 57 ' 57 46 ! *! 5 ! 14 *4 15 14 *! * 5! 57 1' 41 *4 46 1 44 1* 7 16 5 46 11 46 *! * ' * 4! *' 15 *7 44 44 14 47 44 * ' *7 5 11 51 5 47 * 55 *' *1 1 56 ! 4 *5 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 !.*
