Iterasi Fuzzy c Means

7/30/2019 Iterasi Fuzzy c Means

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Matrik X (Langkah 1)

i A(1) B(2) C(3)

1 12 7 9

2 5 4 5

3 8 11 44 10 3 8

5 9 1 3

Inisialisasi Nilai (Langkah 2)

Bangkitkan U (Langkah 3)

i K1 K2

1 0,3 0,7

2 0,2 0,8

3 0,4 0,6

4 0,8 0,2

5 0,4 0,6

Hitung Pusat Kluster (Langkah 4)

i Uik Xij Ui1^w Ui2^w1 2 1 2 3 Ui1w*Xi1

1 0.3 0.7 12 7 9 0.09 0.49 1.08

2 0.2 0.8 5 4 5 0.04 0.64 0.2

3 0.4 0.6 8 11 4 0.16 0.36 1.28

4 0.8 0.2 10 3 8 0.64 0.04 6.4

5 0.4 0.6 9 1 3 0.16 0.36 1.44

1.09 1.89 10.4

Didapat Pusat Kluster Baru

Vkj 1 2 3

1 9.5412844 4.24770642 6.65137615

2 8.25396825 5.51851852 5.52910053

Hitung Fungsi Objektif (5)

Total

i ((Xi1-Vi1)^2)*(Xi2-Vi1)^2 (Xi3-Vi1)^2 i (Xi1-Vi2)^2 (Xi2-Vi2)^2

1 6.04528238 7.57511994 5.516034 19.1364363 1 14.0327538 2.19478738

2 20.623264 0.06135847 2.72704318 23.4116657 2 10.5883094 2.30589849

ITERASI 1

Jumlah

Kluster 1 Kluster 2

(1) Banyaknya cluster yang diinginkan --> c = 2

(2) Pangkat (pembobot) --> w = 2

(3) Maksimum Iterasi --> maxIter = 4

(4) Error terkecil --> e = 0,01

(5) Fungsi Objektif awal --> P0 = 0

(6) Iterasi awal --> iter = 1

Atribut


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3 2.37555761 45.5934686 7.02979547 54.9988216 3 0.06449987 30.0466392

4 0.21042 1.55677132 1.8187863 3.58597761 4 3.04862686 6.34293553

5 0.29298881 10.547597 13.3325478 24.1731336 5 0.55656337 20.4170096

i

(Xij-Vkj)^2 Uik^w P (Xij-Vkj)^2 Uik^w P P Kluster

1 19.1364363 0.09 1.72227927 28.2746844 0.49 13.854595 15.57687462 23.4116657 0.04 0.93646663 13.1741553 0.64 8.4314594 9.36792599

3 54.9988216 0.16 8.79981146 32.4492875 0.36 11.681744 20.481555

4 3.58597761 0.64 2.29502567 15.4969066 0.04 0.6198763 2.91490193

5 24.1731336 0.16 3.86770137 27.3699225 0.36 9.8531721 13.7208735

62.062131

Perbaharui Nilai U (Langkah 6)

i (Xi1-Vi1)^2 (Xi2-Vi1)^2 (Xi3-Vi1)^2 (Xi1-Vi2)^2 (Xi2-Vi2)^2 (Xi3-Vi2)^2 Ui1

1 6.04528238 7.57511994 5.516034 14.0327538 2.1947874 12.047143 47.4111207 0.40362759

2 20.623264 0.06135847 2.72704318 10.5883094 2.3058985 0.2799474 36.5858209 0.6399109

3 2.37555761 45.5934686 7.02979547 0.06449987 30.046639 2.3381484 87.4481092 0.62893094

4 0.21042 1.55677132 1.8187863 3.04862686 6.3429355 6.1053442 19.0828842 0.18791591

5 0.29298881 10.547597 13.3325478 0.55656337 20.41701 6.3963495 51.543056 0.46898914

Didapat U Baru

i K1 K2

1 0.40362 0.59637

2 0.63991 0.36008

3 0.62893 0.37106

4 0.18791 0.81208

5 0.46898 0.53101

Cek Kondisi Berhenti (Langkah 7)

(2) Apakah |P1-P0| < e? : Salah

Kluster 1 Kluster 2

Total P

(1) Apakah Iter > maxIter? : Salah


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Ui1w*Xi2 Ui1w*Xi3 Ui2w*Xi1 Ui2w*Xi2 Ui2w*Xi3

0.63 0.81 5.88 3.43 4.41

0.16 0.2 3.2 2.56 3.2

1.76 0.64 2.88 3.96 1.44

1.92 5.12 0.4 0.12 0.32

0.16 0.48 3.24 0.36 1.08

4.63 7.25 15.6 10.43 10.45

Total

(Xi3-Vi2)^2

12.047143 28.27468

0.2799474 13.17416


4/20

2.3381484 32.44929

6.1053442 15.49691

6.3963495 27.36992

Ui2

0.5963724

0.3600891

0.3710691

0.8120841

0.5310109


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Ui Baru

i K1 K2

1 0.40362 0.59637

2 0.63991 0.36008

3 0.62893 0.371064 0.18791 0.81208

5 0.46898 0.53101


i Uik Xij Ui1^w Ui2^w

1 2 1 2 3 Ui1w*Xi1

1 0.40362 0.59637 12 7 9 0.1629091 0.35565718 1.95490925

2 0.63991 0.36008 5 4 5 0.4094848 0.12965761 2.04742404

3 0.62893 0.37106 8 11 4 0.3955529 0.13768552 3.16442356

4 0.18791 0.81208 10 3 8 0.0353102 0.65947393 0.35310168

5 0.46898 0.53101 9 1 3 0.2199422 0.28197162 1.97948016

umlah 1.2231993 1.56444585 9.4993387


Vkj 1 2 3

1 7.76597809 6.09488438 4.93633866

2 9.68403103 4.33582588 6.72548108


Kluster 1 Total Kluster 2

i (Xi1-Vi1)^2 (Xi2-Vi1)^2 (Xi3-Vi1)^2 i (Xi1-Vi2)^2 (Xi2-Vi2)^21 17.9269415 0.81923428 16.5133435 35.2595193 1 5.36371227 7.09782373

2 7.65063479 4.38854057 0.00405277 12.0432281 2 21.9401467 0.11277902

3 0.05476625 24.0601592 0.87673009 24.9916556 3 2.83596051 44.4112167

4 4.9908539 9.57830934 9.3860208 23.955184 4 0.09983639 1.78443079

5 1.52281008 25.9578469 3.74940741 31.2300644 5 0.46789845 11.1277343

i Kluster 1 Kluster 2


1 35.2595193 0.1629091 5.74409671 17.6349723 0.3556572 6.2720045 12.0161012

2 12.0432281 0.40948481 4.93151896 25.0302107 0.1296576 3.2453572 8.17687616

3 24.9916556 0.39555294 9.88552296 54.6754243 0.1376855 7.5280144 17.4135374

4 23.955184 0.03531017 0.84586158 3.50866565 0.6594739 2.3138735 3.15973509

5 31.2300644 0.21994224 6.86881032 25.4748421 0.2819716 7.1831825 14.0519928

Total P 54.8182426



1 17.9269415 0.81923428 16.5133435 5.36371227 7.0978237 5.1734363 52.8944916 0.66660097

2 7.65063479 4.38854057 0.00405277 21.9401467 0.112779 2.977285 37.0734388 0.32484788

ITERASI 2


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3 0.05476625 24.0601592 0.87673009 2.83596051 44.411217 7.4282471 79.6670799 0.31370116

4 4.9908539 9.57830934 9.3860208 0.09983639 1.7844308 1.6243985 27.4638497 0.87224422

5 1.52281008 25.9578469 3.74940741 0.46789845 11.127734 13.879209 56.7049064 0.55074713

Didapat U Baru

i Ui1 Ui2

1 0.66660097 0.333399032 0.32484788 0.67515212

3 0.31370116 0.68629884

4 0.87224422 0.12775578

5 0.55074713 0.44925287





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1.1403637 1.466182 4.267886 2.4896 3.200915

1.6379392 2.047424 0.648288 0.51863 0.648288

4.3510824 1.582212 1.101484 1.514541 0.550742

0.1059305 0.282481 6.594739 1.978422 5.275791

0.2199422 0.659827 2.537745 0.281972 0.845915

7.4552581 6.038126 15.15014 6.783165 10.52165

Total

(Xi3-Vi2)^25.1734363 17.63497

2.977285 25.03021

7.4282471 54.67542

1.6243985 3.508666

13.879209 25.47484

Ui2

0.333399

0.6751521


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0.6862988

0.1277558

0.4492529


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Ui Baru

i Ui1 Ui2

1 0.66660097 0.33339903

2 0.32484788 0.67515212

3 0.31370116 0.686298844 0.87224422 0.12775578

5 0.55074713 0.44925287



1 2 1 2 3 Ui1w*Xi1

1 0.66660097 0.33339903 12 7 9 0.4443569 0.11115491 5.3322822

2 0.32484788 0.67515212 5 4 5 0.1055261 0.45583038 0.52763074

3 0.31370116 0.68629884 8 11 4 0.0984084 0.47100609 0.78726735

4 0.87224422 0.12775578 10 3 8 0.76081 0.01632154 7.60809972

5 0.55074713 0.44925287 9 1 3 0.3033224 0.20182814 2.72990159

Jumlah 1.7124238 1.25614107 16.9851816


Vkj 1 2 3

1 9.91879564 4.20506157 6.95909688

2 7.45197218 6.3951939 4.69662794




2 24.1945506 0.04205025 3.83806058 28.0746614 2 6.01216755 5.73695382

3 3.68177672 46.1711882 8.75625434 58.6092193 3 0.3003345 21.2042392

4 0.00659415 1.4521734 1.08347931 2.54224685 4 6.49244579 11.5273416

5 0.84418543 10.2724197 15.6744481 26.7910532 5 2.39639014 29.1081172



1 16.3083779 0.44435685 7.24673945 39.5693586 0.1111549 4.3983287 11.6450681

2 28.0746614 0.10552615 2.96261086 11.841156 0.4558304 5.3975586 8.36016949

3 58.6092193 0.09840842 5.76764063 21.9898642 0.4710061 10.35736 16.1250007

4 2.54224685 0.76080997 1.93416676 28.9320544 0.0163215 0.4722157 2.40638245

5 26.7910532 0.3033224 8.12632654 34.3830537 0.2018281 6.9394679 15.0657944

Total P 53.6024152



1 4.33141158 7.81168081 4.16528555 20.6845571 0.3657904 18.519011 55.8777365 0.29185824

2 24.1945506 0.04205025 3.83806058 6.01216755 5.7369538 0.0920346 39.9158174 0.70334677

ITERASI 3


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3 3.68177672 46.1711882 8.75625434 0.3003345 21.204239 0.4852905 80.5990835 0.7271698

4 0.00659415 1.4521734 1.08347931 6.49244579 11.527342 10.912267 31.4743012 0.08077215

5 0.84418543 10.2724197 15.6744481 2.39639014 29.108117 2.8785464 61.174107 0.4379476

Didapat U Baru

i Ui1 Ui2

1 0.29185824 0.708141762 0.70334677 0.29665323

3 0.7271698 0.2728302

4 0.08077215 0.91922785

5 0.4379476 0.5620524





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3.110498 3.999212 1.333859 0.778084 1.000394

0.4221046 0.527631 2.279152 1.823322 2.279152

1.0824926 0.393634 3.768049 5.181067 1.884024

2.2824299 6.08648 0.163215 0.048965 0.130572

0.3033224 0.909967 1.816453 0.201828 0.605484

7.2008475 11.91692 9.360728 8.033266 5.899627

Total

(Xi3-Vi2)^218.519011 39.56936

0.0920346 11.84116

0.4852905 21.98986

10.912267 28.93205

2.8785464 34.38305

Ui2

0.7081418

0.2966532


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0.2728302

0.9192279

0.5620524


13/20

Ui Baru

i Ui1 Ui2

1 0.29185824 0.70814176

2 0.70334677 0.29665323

3 0.7271698 0.27283024 0.08077215 0.91922785

5 0.4379476 0.5620524



1 2 1 2 3 Ui1w*Xi1

1 0.29185824 0.70814176 12 7 9 0.0851812 0.50146475 1.0221748

2 0.70334677 0.29665323 5 4 5 0.4946967 0.08800314 2.47348343

3 0.7271698 0.2728302 8 11 4 0.5287759 0.07443632 4.23020732

4 0.08077215 0.91922785 10 3 8 0.0065241 0.84497985 0.0652414

5 0.4379476 0.5620524 9 1 3 0.1917981 0.3159029 1.72618289

Jumlah 1.3069761 1.82478695 9.51728984


Vkj 1 2 3

1 7.28191589 6.58234006 4.57759383

2 10.0537807 4.12755458 7.10137211




2 5.20714015 6.6684802 0.17842698 12.0540473 2 25.5406991 0.01627017

3 0.51564478 19.5157193 0.33361463 20.3649787 3 4.21801507 47.2305061

4 7.38798121 12.8331603 11.712864 31.9340055 4 0.00289236 1.27137932

5 2.95181299 31.1625206 2.48880228 36.6031358 5 1.11045372 9.78159763



1 41.9924338 0.08518123 3.5769673 15.6435002 0.5014647 7.8446639 11.4216312

2 12.0540473 0.49469669 5.96309725 29.9727341 0.0880031 2.6376946 8.60079185

3 20.3649787 0.52877592 10.7685103 61.0670301 0.0744363 4.5456049 15.3141152

4 31.9340055 0.00652414 0.20834191 2.08180376 0.8449798 1.7590822 1.96742414

5 36.6031358 0.1917981 7.02041187 27.7133046 0.3159029 8.7547133 15.7751252

Total P 53.0790876



1 22.2603176 0.17443982 19.5576764 3.78776965 8.2509427 3.6047879 57.635934 0.72858078

2 5.20714015 6.6684802 0.17842698 25.5406991 0.0162702 4.4157648 42.0267814 0.28681824

ITERASI 4


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3 0.51564478 19.5157193 0.33361463 4.21801507 47.230506 9.618509 81.4320089 0.25008567

4 7.38798121 12.8331603 11.712864 0.00289236 1.2713793 0.8075321 34.0158093 0.93879893

5 2.95181299 31.1625206 2.48880228 1.11045372 9.7815976 16.821253 64.3164404 0.5691101

Didapat U Baru

i Ui1 Ui2

1 0.72858078 0.271419222 0.28681824 0.71318176

3 0.25008567 0.74991433

4 0.93879893 0.06120107

5 0.5691101 0.4308899





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0.5962686 0.766631 6.017577 3.510253 4.513183

1.9787867 2.473483 0.440016 0.352013 0.440016

5.8165351 2.115104 0.595491 0.8188 0.297745

0.0195724 0.052193 8.449798 2.53494 6.759839

0.1917981 0.575394 2.843126 0.315903 0.947709

8.602961 5.982806 18.34601 7.531908 12.95849

Total

(Xi3-Vi2)^23.6047879 15.6435

4.4157648 29.97273

9.618509 61.06703

0.8075321 2.081804

16.821253 27.7133

Ui2

0.2714192

0.7131818


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0.7499143

0.0612011

0.4308899


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Ui Baru

i Ui1 Ui2

1 0.72858078 0.27141922

2 0.28681824 0.71318176

3 0.25008567 0.749914334 0.93879893 0.06120107

5 0.5691101 0.4308899



1 2 1 2 3 Ui1w*Xi1

1 0.72858078 0.27141922 12 7 9 0.53083 0.07366839 6.36995945

2 0.28681824 0.71318176 5 4 5 0.0822647 0.50862823 0.4113235

3 0.25008567 0.74991433 8 11 4 0.0625428 0.5623715 0.50034275

4 0.93879893 0.06120107 10 3 8 0.8813434 0.00374557 8.8134344

5 0.5691101 0.4308899 9 1 3 0.3238863 0.18566611 2.91497676

Jumlah 1.8808672 1.33407979 19.0100369


Vkj 1 2 3

1 10.1070593 4.09425833 7.15700214

2 7.22189522 6.69613691 4.52941838




2 26.0820551 0.00888463 4.65265825 30.743598 2 4.93681836 7.26915425

3 4.43969907 47.689268 9.96666254 62.0956296 3 0.60544705 18.5232375

4 0.0114617 1.1974013 0.71064539 1.91950839 4 7.71786618 13.6614281

5 1.22558039 9.57443463 17.2806668 28.0806818 5 3.16165661 32.4459757



1 15.4232001 0.53082995 8.18709658 42.9087181 0.0736684 3.1610163 11.3481129

2 30.743598 0.0822647 2.52911289 12.4274197 0.5086282 6.3209364 8.85004933

3 62.0956296 0.06254284 3.88363726 19.4089684 0.5623715 10.915051 14.7986879

4 1.91950839 0.88134344 1.69174612 33.424231 0.0037456 0.1251928 1.81693893

5 28.0806818 0.32388631 9.09494832 37.9467529 0.1856661 7.0454258 16.1403742

Total P 52.9541632



1 3.58322433 8.44333464 3.3966411 22.8302853 0.0923328 19.9861 58.3319181 0.26440413

2 26.0820551 0.00888463 4.65265825 4.93681836 7.2691542 0.2214471 43.1710177 0.71213512

ITERASI 5


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3 4.43969907 47.689268 9.96666254 0.60544705 18.523237 0.2802838 81.5045979 0.76186658

4 0.0114617 1.1974013 0.71064539 7.71786618 13.661428 12.044937 35.3437394 0.05430971

5 1.22558039 9.57443463 17.2806668 3.16165661 32.445976 2.3391206 66.0274348 0.42528809

Didapat U Baru

i Ui1 Ui2

1 0.26440413 0.735595872 0.71213512 0.28786488

3 0.76186658 0.23813342

4 0.05430971 0.94569029

5 0.42528809 0.57471191


Berdasarkan hasil pembaharuan matrix U maka dapat disimpulkan

kecenderungan suatu data akan masuk ke dalam cluster yang mana

dengan melihat derajat keanggotaan (Uik) yang tertinggi dari setiap cluster

Vkj 1 2 3

1 10.1070593 4.09425833 7.15700214

2 7.22189522 6.69613691 4.52941838

i Ui1 Ui2

1 0.26440413 0.73559587

2 0.71213512 0.287864883 0.76186658 0.23813342

4 0.05430971 0.94569029

5 0.42528809 0.57471191

1 2

1 X

2 X

3 X

4 X

5 X

(1) Apakah Iter > maxIter? : Benar | Iterasi Dihentikan

(2) Apakah |P1-P0| < e? : Benar | Iterasi Dihentikan

iCluster


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3.7158097 4.77747 0.884021 0.515679 0.663016

0.3290588 0.411324 2.543141 2.034513 2.543141

0.6879713 0.250171 4.498972 6.186086 2.249486

2.6440303 7.050748 0.037456 0.011237 0.029965

0.3238863 0.971659 1.670995 0.185666 0.556998

7.7007564 13.46137 9.634584 8.933181 6.042606

Total

(Xi3-Vi2)^219.9861 42.90872

0.2214471 12.42742

0.2802838 19.40897

12.044937 33.42423

2.3391206 37.94675

Ui2

0.7355959

0.2878649


20/20

0.2381334

0.9456903

0.5747119

Iterasi Fuzzy c Means

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