#### September 3rd, 2016

advclust is package for advance clustering. Right now advclust provide several Fuzzy Clustering and Consensus Fuzzy Clustering. This package use Object Oriented Programming (S4 for R). Several Algorithms that provided by this package are: - Fuzzy C-Means (FCM) - Gustafson Kessel (GK) - Gath Geva (GG) - Sum Voting Consensus - Product Voting Consensus - Borda Voting Consensus

## Fuzzy Clustering Analysis

### Fuzzy C-Means

fuzzy.CM() perform fuzzy c-means analysis. More description of this function (parameter setting, description, and return value) explained via ?fuzzy.CM This algorithm used to get sperichal cluster

library(advclust)
data(iris)
fuzzy.CM(X=iris[,1:4],K = 3,m = 2,RandomNumber = 1234)->cl_CM
## Maximum Iteration 1000 will be used.
## Default threshold 1e-9 will be used.
##
## Membership initialiazed randomly
##
##
iteration:  1
iteration:  2
iteration:  3
iteration:  4
iteration:  5
iteration:  6
iteration:  7
iteration:  8
iteration:  9
iteration:  10
iteration:  11
iteration:  12
iteration:  13
iteration:  14
iteration:  15
iteration:  16
iteration:  17
iteration:  18
iteration:  19
iteration:  20
iteration:  21
iteration:  22
iteration:  23
iteration:  24
iteration:  25
iteration:  26
iteration:  27
iteration:  28
iteration:  29
iteration:  30
iteration:  31
iteration:  32
iteration:  33
iteration:  34
iteration:  35
iteration:  36
iteration:  37
iteration:  38
iteration:  39
iteration:  40
iteration:  41
iteration:  42
iteration:  43
iteration:  44
iteration:  45
iteration:  46
iteration:  47
iteration:  48
iteration:  49
## Finish :)
show(cl_CM)
## Function call: fuzzy.CM(X = iris[, 1:4], K = 3, m = 2, RandomNumber = 1234)
## Fuzzy C-Means
## Function objective: 60.5057106294886
## Membership & Label Matrix:
##
##            Cluster 1   Cluster 2   Cluster 3   Label
## --------  ----------  ----------  ----------  ------
## Obs 1          0.002       0.997       0.001       2
## Obs 2          0.017       0.976       0.007       2
## Obs 3          0.014       0.980       0.006       2
## Obs 4          0.022       0.967       0.010       2
## Obs 5          0.004       0.994       0.002       2
## Obs 6          0.045       0.935       0.021       2
## Obs 7          0.014       0.979       0.007       2
## Obs 8          0.000       1.000       0.000       2
## Obs 9          0.048       0.930       0.022       2
## Obs 10         0.012       0.983       0.005       2
## Obs 11         0.022       0.968       0.010       2
## Obs 12         0.005       0.992       0.002       2
## Obs 13         0.020       0.971       0.009       2
## Obs 14         0.052       0.923       0.025       2
## Obs 15         0.073       0.890       0.038       2
## Obs 16         0.104       0.841       0.054       2
## Obs 17         0.036       0.947       0.017       2
## Obs 18         0.002       0.997       0.001       2
## Obs 19         0.066       0.904       0.030       2
## Obs 20         0.014       0.979       0.007       2
## Obs 21         0.022       0.969       0.010       2
## Obs 22         0.010       0.985       0.005       2
## Obs 23         0.028       0.959       0.014       2
## Obs 24         0.014       0.979       0.006       2
## Obs 25         0.023       0.967       0.010       2
## Obs 26         0.018       0.974       0.008       2
## Obs 27         0.004       0.995       0.002       2
## Obs 28         0.005       0.993       0.002       2
## Obs 29         0.004       0.994       0.002       2
## Obs 30         0.014       0.980       0.006       2
## Obs 31         0.015       0.979       0.006       2
## Obs 32         0.018       0.974       0.008       2
## Obs 33         0.041       0.939       0.020       2
## Obs 34         0.063       0.904       0.032       2
## Obs 35         0.010       0.985       0.005       2
## Obs 36         0.010       0.985       0.005       2
## Obs 37         0.024       0.964       0.012       2
## Obs 38         0.006       0.991       0.003       2
## Obs 39         0.041       0.940       0.019       2
## Obs 40         0.001       0.998       0.001       2
## Obs 41         0.004       0.995       0.002       2
## Obs 42         0.102       0.851       0.047       2
## Obs 43         0.032       0.953       0.015       2
## Obs 44         0.014       0.979       0.006       2
## Obs 45         0.038       0.945       0.017       2
## Obs 46         0.019       0.972       0.009       2
## Obs 47         0.016       0.977       0.007       2
## Obs 48         0.018       0.974       0.008       2
## Obs 49         0.016       0.977       0.007       2
## Obs 50         0.002       0.997       0.001       2
## Obs 51         0.454       0.045       0.501       3
## Obs 52         0.764       0.029       0.207       1
## Obs 53         0.369       0.031       0.600       3
## Obs 54         0.870       0.049       0.080       1
## Obs 55         0.759       0.024       0.217       1
## Obs 56         0.974       0.006       0.020       1
## Obs 57         0.673       0.030       0.297       1
## Obs 58         0.583       0.285       0.132       1
## Obs 59         0.721       0.031       0.248       1
## Obs 60         0.831       0.075       0.095       1
## Obs 61         0.637       0.218       0.145       1
## Obs 62         0.962       0.009       0.029       1
## Obs 63         0.843       0.056       0.101       1
## Obs 64         0.900       0.012       0.088       1
## Obs 65         0.816       0.092       0.092       1
## Obs 66         0.690       0.042       0.268       1
## Obs 67         0.933       0.014       0.053       1
## Obs 68         0.926       0.026       0.048       1
## Obs 69         0.835       0.027       0.137       1
## Obs 70         0.878       0.052       0.071       1
## Obs 71         0.722       0.028       0.251       1
## Obs 72         0.934       0.019       0.046       1
## Obs 73         0.705       0.024       0.271       1
## Obs 74         0.903       0.014       0.083       1
## Obs 75         0.876       0.023       0.101       1
## Obs 76         0.755       0.034       0.211       1
## Obs 77         0.524       0.034       0.443       1
## Obs 78         0.306       0.021       0.672       3
## Obs 79         0.969       0.005       0.026       1
## Obs 80         0.767       0.128       0.105       1
## Obs 81         0.832       0.078       0.090       1
## Obs 82         0.795       0.104       0.101       1
## Obs 83         0.919       0.031       0.050       1
## Obs 84         0.656       0.024       0.320       1
## Obs 85         0.891       0.026       0.082       1
## Obs 86         0.797       0.032       0.171       1
## Obs 87         0.555       0.033       0.411       1
## Obs 88         0.858       0.027       0.115       1
## Obs 89         0.929       0.024       0.047       1
## Obs 90         0.899       0.038       0.062       1
## Obs 91         0.931       0.020       0.049       1
## Obs 92         0.916       0.012       0.073       1
## Obs 93         0.936       0.023       0.042       1
## Obs 94         0.598       0.269       0.133       1
## Obs 95         0.959       0.013       0.028       1
## Obs 96         0.946       0.017       0.038       1
## Obs 97         0.967       0.010       0.023       1
## Obs 98         0.944       0.011       0.045       1
## Obs 99         0.520       0.355       0.125       1
## Obs 100        0.961       0.013       0.027       1
## Obs 101        0.121       0.019       0.860       3
## Obs 102        0.616       0.029       0.355       1
## Obs 103        0.038       0.006       0.956       3
## Obs 104        0.142       0.013       0.846       3
## Obs 105        0.038       0.005       0.958       3
## Obs 106        0.153       0.035       0.812       3
## Obs 107        0.760       0.073       0.167       1
## Obs 108        0.115       0.022       0.863       3
## Obs 109        0.117       0.014       0.869       3
## Obs 110        0.115       0.024       0.861       3
## Obs 111        0.210       0.017       0.773       3
## Obs 112        0.223       0.016       0.761       3
## Obs 113        0.010       0.001       0.989       3
## Obs 114        0.660       0.034       0.306       1
## Obs 115        0.461       0.038       0.501       3
## Obs 116        0.136       0.014       0.850       3
## Obs 117        0.080       0.007       0.913       3
## Obs 118        0.186       0.051       0.764       3
## Obs 119        0.193       0.049       0.758       3
## Obs 120        0.711       0.032       0.257       1
## Obs 121        0.026       0.004       0.970       3
## Obs 122        0.707       0.034       0.259       1
## Obs 123        0.175       0.042       0.783       3
## Obs 124        0.596       0.023       0.381       1
## Obs 125        0.022       0.003       0.975       3
## Obs 126        0.075       0.013       0.912       3
## Obs 127        0.708       0.021       0.271       1
## Obs 128        0.647       0.023       0.330       1
## Obs 129        0.083       0.008       0.909       3
## Obs 130        0.095       0.014       0.891       3
## Obs 131        0.107       0.020       0.873       3
## Obs 132        0.189       0.051       0.760       3
## Obs 133        0.085       0.009       0.906       3
## Obs 134        0.540       0.023       0.436       1
## Obs 135        0.393       0.031       0.576       3
## Obs 136        0.132       0.029       0.840       3
## Obs 137        0.129       0.017       0.854       3
## Obs 138        0.110       0.010       0.880       3
## Obs 139        0.750       0.022       0.228       1
## Obs 140        0.029       0.003       0.968       3
## Obs 141        0.038       0.005       0.957       3
## Obs 142        0.129       0.015       0.855       3
## Obs 143        0.616       0.029       0.355       1
## Obs 144        0.034       0.005       0.961       3
## Obs 145        0.063       0.010       0.927       3
## Obs 146        0.106       0.011       0.882       3
## Obs 147        0.508       0.026       0.467       1
## Obs 148        0.156       0.012       0.831       3
## Obs 149        0.189       0.022       0.789       3
## Obs 150        0.582       0.027       0.391       1
##
## Centroid:
##
##              Sepal.Length   Sepal.Width   Petal.Length   Petal.Width
## ----------  -------------  ------------  -------------  ------------
## Cluster 1           5.889         2.761          4.364         1.397
## Cluster 2           5.004         3.414          1.483         0.254
## Cluster 3           6.775         3.052          5.647         2.054

### Gustafson Kessel

fuzzy.GK() perform Gustafson Kessel analysis. More description of this function (parameter setting, description, and return value) explained via ?fuzzy.GK. This algorithm used to get ellipsodial and sperichal cluster

library(advclust)
data(iris)
fuzzy.GK(X=iris[,1:4],K = 3,m = 2,RandomNumber = 1234)->cl_GK
## Default Gamma (0) will be used
## Default rho will be used
## Maximum Iteration 1000 will be used.
## Default threshold 1e-9 will be used.
##
## Membership initialiazed randomly
##
##
iteration:  1
iteration:  2
iteration:  3
iteration:  4
iteration:  5
iteration:  6
iteration:  7
iteration:  8
iteration:  9
iteration:  10
iteration:  11
iteration:  12
iteration:  13
iteration:  14
iteration:  15
iteration:  16
iteration:  17
iteration:  18
iteration:  19
iteration:  20
iteration:  21
iteration:  22
iteration:  23
iteration:  24
iteration:  25
iteration:  26
iteration:  27
iteration:  28
iteration:  29
iteration:  30
iteration:  31
iteration:  32
iteration:  33
iteration:  34
iteration:  35
iteration:  36
iteration:  37
iteration:  38
iteration:  39
iteration:  40
iteration:  41
iteration:  42
iteration:  43
iteration:  44
iteration:  45
iteration:  46
iteration:  47
iteration:  48
iteration:  49
iteration:  50
iteration:  51
iteration:  52
iteration:  53
iteration:  54
iteration:  55
iteration:  56
iteration:  57
iteration:  58
iteration:  59
iteration:  60
iteration:  61
iteration:  62
iteration:  63
iteration:  64
iteration:  65
iteration:  66
iteration:  67
iteration:  68
iteration:  69
iteration:  70
iteration:  71
iteration:  72
iteration:  73
iteration:  74
iteration:  75
iteration:  76
iteration:  77
iteration:  78
iteration:  79
iteration:  80
iteration:  81
iteration:  82
iteration:  83
iteration:  84
iteration:  85
iteration:  86
iteration:  87
iteration:  88
iteration:  89
iteration:  90
iteration:  91
iteration:  92
iteration:  93
iteration:  94
iteration:  95
iteration:  96
iteration:  97
iteration:  98
iteration:  99
iteration:  100
iteration:  101
iteration:  102
iteration:  103
iteration:  104
iteration:  105
iteration:  106
iteration:  107
iteration:  108
iteration:  109
iteration:  110
iteration:  111
iteration:  112
iteration:  113
iteration:  114
iteration:  115
iteration:  116
iteration:  117
iteration:  118
iteration:  119
iteration:  120
iteration:  121
iteration:  122
iteration:  123
iteration:  124
iteration:  125
iteration:  126
iteration:  127
iteration:  128
iteration:  129
iteration:  130
iteration:  131
iteration:  132
iteration:  133
iteration:  134
iteration:  135
iteration:  136
iteration:  137
iteration:  138
iteration:  139
iteration:  140
iteration:  141
iteration:  142
iteration:  143
iteration:  144
iteration:  145
iteration:  146
iteration:  147
iteration:  148
iteration:  149
iteration:  150
iteration:  151
iteration:  152
iteration:  153
iteration:  154
iteration:  155
iteration:  156
iteration:  157
iteration:  158
iteration:  159
iteration:  160
iteration:  161
iteration:  162
iteration:  163
iteration:  164
iteration:  165
iteration:  166
iteration:  167
iteration:  168
iteration:  169
iteration:  170
iteration:  171
iteration:  172
iteration:  173
iteration:  174
iteration:  175
iteration:  176
iteration:  177
iteration:  178
iteration:  179
iteration:  180
iteration:  181
iteration:  182
iteration:  183
iteration:  184
iteration:  185
iteration:  186
iteration:  187
iteration:  188
iteration:  189
iteration:  190
iteration:  191
iteration:  192
iteration:  193
iteration:  194
iteration:  195
iteration:  196
iteration:  197
iteration:  198
iteration:  199
iteration:  200
iteration:  201
iteration:  202
iteration:  203
iteration:  204
iteration:  205
iteration:  206
iteration:  207
iteration:  208
iteration:  209
iteration:  210
iteration:  211
iteration:  212
iteration:  213
iteration:  214
iteration:  215
## Finish :)
show(cl_GK)
## Function call: fuzzy.GK(X = iris[, 1:4], K = 3, m = 2, RandomNumber = 1234)
## Gustafson Kessel Clustering
## Function objective: 31.5266810464968
## Membership & Label Matrix:
##
##            Cluster 1   Cluster 2   Cluster 3   Label
## --------  ----------  ----------  ----------  ------
## Obs 1          0.003       0.995       0.001       2
## Obs 2          0.032       0.957       0.011       2
## Obs 3          0.015       0.979       0.005       2
## Obs 4          0.024       0.967       0.009       2
## Obs 5          0.006       0.992       0.002       2
## Obs 6          0.027       0.962       0.011       2
## Obs 7          0.041       0.944       0.015       2
## Obs 8          0.003       0.995       0.001       2
## Obs 9          0.051       0.932       0.017       2
## Obs 10         0.037       0.948       0.015       2
## Obs 11         0.015       0.979       0.006       2
## Obs 12         0.021       0.970       0.009       2
## Obs 13         0.037       0.949       0.014       2
## Obs 14         0.075       0.899       0.026       2
## Obs 15         0.050       0.929       0.022       2
## Obs 16         0.040       0.942       0.018       2
## Obs 17         0.042       0.942       0.016       2
## Obs 18         0.007       0.990       0.003       2
## Obs 19         0.036       0.949       0.015       2
## Obs 20         0.014       0.980       0.006       2
## Obs 21         0.047       0.933       0.020       2
## Obs 22         0.027       0.963       0.010       2
## Obs 23         0.074       0.898       0.028       2
## Obs 24         0.088       0.884       0.028       2
## Obs 25         0.081       0.879       0.041       2
## Obs 26         0.050       0.932       0.018       2
## Obs 27         0.029       0.961       0.010       2
## Obs 28         0.008       0.989       0.003       2
## Obs 29         0.013       0.982       0.005       2
## Obs 30         0.026       0.964       0.010       2
## Obs 31         0.025       0.965       0.009       2
## Obs 32         0.052       0.929       0.019       2
## Obs 33         0.042       0.937       0.021       2
## Obs 34         0.027       0.960       0.013       2
## Obs 35         0.018       0.976       0.006       2
## Obs 36         0.036       0.952       0.012       2
## Obs 37         0.045       0.938       0.018       2
## Obs 38         0.023       0.967       0.010       2
## Obs 39         0.049       0.935       0.016       2
## Obs 40         0.006       0.992       0.002       2
## Obs 41         0.018       0.976       0.006       2
## Obs 42         0.229       0.710       0.061       2
## Obs 43         0.050       0.932       0.018       2
## Obs 44         0.132       0.823       0.045       2
## Obs 45         0.064       0.908       0.028       2
## Obs 46         0.041       0.947       0.012       2
## Obs 47         0.022       0.968       0.010       2
## Obs 48         0.019       0.974       0.007       2
## Obs 49         0.010       0.986       0.004       2
## Obs 50         0.006       0.992       0.002       2
## Obs 51         0.724       0.029       0.247       1
## Obs 52         0.788       0.015       0.197       1
## Obs 53         0.777       0.013       0.210       1
## Obs 54         0.700       0.025       0.274       1
## Obs 55         0.756       0.011       0.234       1
## Obs 56         0.631       0.019       0.351       1
## Obs 57         0.688       0.017       0.295       1
## Obs 58         0.772       0.052       0.176       1
## Obs 59         0.791       0.015       0.194       1
## Obs 60         0.589       0.032       0.378       1
## Obs 61         0.676       0.068       0.257       1
## Obs 62         0.692       0.019       0.289       1
## Obs 63         0.648       0.051       0.302       1
## Obs 64         0.805       0.007       0.188       1
## Obs 65         0.749       0.043       0.208       1
## Obs 66         0.753       0.027       0.220       1
## Obs 67         0.542       0.021       0.438       1
## Obs 68         0.639       0.042       0.319       1
## Obs 69         0.530       0.036       0.433       1
## Obs 70         0.852       0.016       0.132       1
## Obs 71         0.314       0.017       0.669       3
## Obs 72         0.840       0.018       0.142       1
## Obs 73         0.676       0.009       0.315       1
## Obs 74         0.567       0.026       0.406       1
## Obs 75         0.850       0.014       0.136       1
## Obs 76         0.780       0.020       0.200       1
## Obs 77         0.742       0.015       0.244       1
## Obs 78         0.598       0.008       0.393       1
## Obs 79         0.817       0.005       0.177       1
## Obs 80         0.836       0.037       0.127       1
## Obs 81         0.840       0.019       0.141       1
## Obs 82         0.803       0.030       0.167       1
## Obs 83         0.932       0.008       0.061       1
## Obs 84         0.485       0.009       0.505       3
## Obs 85         0.478       0.030       0.492       3
## Obs 86         0.597       0.033       0.370       1
## Obs 87         0.801       0.012       0.187       1
## Obs 88         0.654       0.030       0.317       1
## Obs 89         0.753       0.023       0.224       1
## Obs 90         0.798       0.014       0.188       1
## Obs 91         0.559       0.028       0.413       1
## Obs 92         0.831       0.008       0.162       1
## Obs 93         0.928       0.007       0.066       1
## Obs 94         0.784       0.050       0.166       1
## Obs 95         0.830       0.009       0.161       1
## Obs 96         0.693       0.032       0.275       1
## Obs 97         0.820       0.013       0.167       1
## Obs 98         0.923       0.006       0.071       1
## Obs 99         0.703       0.097       0.201       1
## Obs 100        0.910       0.006       0.084       1
## Obs 101        0.165       0.018       0.817       3
## Obs 102        0.180       0.011       0.810       3
## Obs 103        0.242       0.007       0.751       3
## Obs 104        0.440       0.011       0.549       3
## Obs 105        0.109       0.006       0.886       3
## Obs 106        0.601       0.013       0.386       1
## Obs 107        0.347       0.043       0.610       3
## Obs 108        0.618       0.015       0.366       1
## Obs 109        0.549       0.014       0.437       1
## Obs 110        0.173       0.015       0.812       3
## Obs 111        0.137       0.008       0.855       3
## Obs 112        0.159       0.005       0.836       3
## Obs 113        0.068       0.004       0.928       3
## Obs 114        0.209       0.022       0.769       3
## Obs 115        0.127       0.026       0.847       3
## Obs 116        0.062       0.007       0.931       3
## Obs 117        0.452       0.006       0.542       3
## Obs 118        0.604       0.022       0.374       1
## Obs 119        0.520       0.024       0.456       1
## Obs 120        0.562       0.023       0.415       1
## Obs 121        0.063       0.005       0.932       3
## Obs 122        0.143       0.015       0.842       3
## Obs 123        0.619       0.018       0.364       1
## Obs 124        0.207       0.009       0.784       3
## Obs 125        0.198       0.007       0.794       3
## Obs 126        0.663       0.011       0.326       1
## Obs 127        0.167       0.007       0.826       3
## Obs 128        0.161       0.005       0.834       3
## Obs 129        0.116       0.006       0.878       3
## Obs 130        0.626       0.016       0.359       1
## Obs 131        0.587       0.013       0.401       1
## Obs 132        0.646       0.024       0.330       1
## Obs 133        0.099       0.007       0.894       3
## Obs 134        0.675       0.007       0.318       1
## Obs 135        0.445       0.039       0.516       3
## Obs 136        0.281       0.020       0.699       3
## Obs 137        0.120       0.014       0.866       3
## Obs 138        0.457       0.009       0.534       3
## Obs 139        0.174       0.007       0.818       3
## Obs 140        0.124       0.008       0.869       3
## Obs 141        0.059       0.007       0.934       3
## Obs 142        0.168       0.030       0.802       3
## Obs 143        0.180       0.011       0.810       3
## Obs 144        0.082       0.005       0.914       3
## Obs 145        0.070       0.009       0.921       3
## Obs 146        0.118       0.018       0.865       3
## Obs 147        0.244       0.018       0.738       3
## Obs 148        0.037       0.002       0.961       3
## Obs 149        0.132       0.015       0.853       3
## Obs 150        0.266       0.011       0.723       3
##
## Centroid:
##
##              Sepal.Length   Sepal.Width   Petal.Length   Petal.Width
## ----------  -------------  ------------  -------------  ------------
## Cluster 1           6.128         2.802          4.510         1.402
## Cluster 2           5.014         3.438          1.465         0.244
## Cluster 3           6.398         2.975          5.305         2.015

### Gath Geva

fuzzy.GG() perform Gath Geva analysis. More description of this function (parameter setting, description, and return value) explained via ?fuzzy.GG This algorithm used to get hyperellipsodial cluster. Use membership that resulted from fuzzy.CM as initial membership to get best result.

library(advclust)
data(iris)
fuzzy.GG(X=iris[,1:4],K = 3,m = 2,RandomNumber = 1234)->cl_GG
## Maximum Iteration 1000 will be used.
## Default threshold 1e-9 will be used.
##
## Membership initialiazed randomly
##
##
iteration:  1
iteration:  2
iteration:  3
iteration:  4
iteration:  5
iteration:  6
iteration:  7
iteration:  8
iteration:  9
iteration:  10
iteration:  11
iteration:  12
iteration:  13
iteration:  14
iteration:  15
iteration:  16
iteration:  17
iteration:  18
iteration:  19
iteration:  20
iteration:  21
iteration:  22
iteration:  23
iteration:  24
iteration:  25
iteration:  26
iteration:  27
iteration:  28
iteration:  29
iteration:  30
iteration:  31
iteration:  32
iteration:  33
iteration:  34
iteration:  35
iteration:  36
iteration:  37
iteration:  38
iteration:  39
iteration:  40
iteration:  41
iteration:  42
iteration:  43
iteration:  44
iteration:  45
iteration:  46
iteration:  47
iteration:  48
iteration:  49
iteration:  50
iteration:  51
iteration:  52
iteration:  53
iteration:  54
iteration:  55
iteration:  56
iteration:  57
iteration:  58
iteration:  59
iteration:  60
iteration:  61
iteration:  62
iteration:  63
iteration:  64
iteration:  65
iteration:  66
iteration:  67
iteration:  68
iteration:  69
iteration:  70
iteration:  71
iteration:  72
iteration:  73
iteration:  74
iteration:  75
iteration:  76
iteration:  77
iteration:  78
iteration:  79
iteration:  80
iteration:  81
iteration:  82
iteration:  83
iteration:  84
iteration:  85
iteration:  86
iteration:  87
iteration:  88
iteration:  89
iteration:  90
iteration:  91
iteration:  92
iteration:  93
iteration:  94
iteration:  95
iteration:  96
iteration:  97
iteration:  98
iteration:  99
iteration:  100
iteration:  101
iteration:  102
iteration:  103
iteration:  104
iteration:  105
iteration:  106
iteration:  107
iteration:  108
iteration:  109
iteration:  110
iteration:  111
iteration:  112
iteration:  113
iteration:  114
iteration:  115
iteration:  116
iteration:  117
iteration:  118
iteration:  119
iteration:  120
iteration:  121
iteration:  122
iteration:  123
iteration:  124
iteration:  125
iteration:  126
iteration:  127
iteration:  128
iteration:  129
iteration:  130
iteration:  131
iteration:  132
iteration:  133
iteration:  134
iteration:  135
iteration:  136
iteration:  137
iteration:  138
iteration:  139
iteration:  140
iteration:  141
iteration:  142
iteration:  143
iteration:  144
iteration:  145
iteration:  146
iteration:  147
iteration:  148
iteration:  149
iteration:  150
iteration:  151
iteration:  152
iteration:  153
iteration:  154
iteration:  155
iteration:  156
iteration:  157
iteration:  158
iteration:  159
iteration:  160
iteration:  161
iteration:  162
iteration:  163
iteration:  164
iteration:  165
iteration:  166
iteration:  167
iteration:  168
iteration:  169
iteration:  170
iteration:  171
iteration:  172
iteration:  173
iteration:  174
iteration:  175
iteration:  176
iteration:  177
iteration:  178
iteration:  179
iteration:  180
iteration:  181
iteration:  182
iteration:  183
iteration:  184
iteration:  185
iteration:  186
iteration:  187
iteration:  188
iteration:  189
iteration:  190
iteration:  191
iteration:  192
iteration:  193
iteration:  194
iteration:  195
iteration:  196
iteration:  197
iteration:  198
iteration:  199
iteration:  200
iteration:  201
iteration:  202
iteration:  203
iteration:  204
iteration:  205
iteration:  206
iteration:  207
## Finish :)
show(cl_GG)
## Function call: fuzzy.GG(X = iris[, 1:4], K = 3, m = 2, RandomNumber = 1234)
## Gath Geva Clustering
## Function objective: 6.37182273445943e+60
## Membership & Label Matrix:
##
##            Cluster 1   Cluster 2   Cluster 3   Label
## --------  ----------  ----------  ----------  ------
## Obs 1          0.004       0.995       0.001       2
## Obs 2          0.048       0.940       0.012       2
## Obs 3          0.017       0.979       0.004       2
## Obs 4          0.035       0.955       0.010       2
## Obs 5          0.006       0.992       0.002       2
## Obs 6          0.025       0.966       0.008       2
## Obs 7          0.053       0.932       0.015       2
## Obs 8          0.005       0.993       0.002       2
## Obs 9          0.073       0.909       0.018       2
## Obs 10         0.050       0.934       0.015       2
## Obs 11         0.021       0.973       0.007       2
## Obs 12         0.029       0.961       0.009       2
## Obs 13         0.052       0.934       0.015       2
## Obs 14         0.065       0.918       0.017       2
## Obs 15         0.058       0.921       0.020       2
## Obs 16         0.056       0.923       0.021       2
## Obs 17         0.055       0.927       0.018       2
## Obs 18         0.011       0.986       0.003       2
## Obs 19         0.040       0.947       0.013       2
## Obs 20         0.020       0.973       0.007       2
## Obs 21         0.050       0.933       0.016       2
## Obs 22         0.033       0.958       0.010       2
## Obs 23         0.052       0.934       0.015       2
## Obs 24         0.055       0.932       0.014       2
## Obs 25         0.089       0.877       0.034       2
## Obs 26         0.057       0.927       0.016       2
## Obs 27         0.019       0.976       0.005       2
## Obs 28         0.011       0.986       0.003       2
## Obs 29         0.019       0.976       0.005       2
## Obs 30         0.034       0.956       0.010       2
## Obs 31         0.028       0.963       0.008       2
## Obs 32         0.066       0.916       0.019       2
## Obs 33         0.055       0.923       0.022       2
## Obs 34         0.034       0.953       0.013       2
## Obs 35         0.024       0.969       0.007       2
## Obs 36         0.042       0.947       0.011       2
## Obs 37         0.060       0.921       0.019       2
## Obs 38         0.026       0.965       0.009       2
## Obs 39         0.064       0.920       0.016       2
## Obs 40         0.008       0.989       0.003       2
## Obs 41         0.021       0.973       0.006       2
## Obs 42         0.281       0.654       0.065       2
## Obs 43         0.061       0.922       0.017       2
## Obs 44         0.132       0.832       0.036       2
## Obs 45         0.052       0.930       0.018       2
## Obs 46         0.057       0.930       0.013       2
## Obs 47         0.032       0.956       0.012       2
## Obs 48         0.027       0.965       0.007       2
## Obs 49         0.014       0.981       0.005       2
## Obs 50         0.008       0.989       0.002       2
## Obs 51         0.615       0.192       0.193       1
## Obs 52         0.698       0.147       0.155       1
## Obs 53         0.716       0.108       0.176       1
## Obs 54         0.547       0.226       0.227       1
## Obs 55         0.699       0.102       0.199       1
## Obs 56         0.588       0.158       0.254       1
## Obs 57         0.624       0.150       0.226       1
## Obs 58         0.551       0.324       0.126       1
## Obs 59         0.732       0.114       0.154       1
## Obs 60         0.527       0.202       0.271       1
## Obs 61         0.441       0.371       0.188       1
## Obs 62         0.627       0.163       0.210       1
## Obs 63         0.514       0.248       0.238       1
## Obs 64         0.799       0.064       0.136       1
## Obs 65         0.577       0.287       0.136       1
## Obs 66         0.626       0.205       0.169       1
## Obs 67         0.527       0.156       0.317       1
## Obs 68         0.531       0.255       0.215       1
## Obs 69         0.417       0.247       0.336       1
## Obs 70         0.717       0.165       0.118       1
## Obs 71         0.332       0.127       0.541       3
## Obs 72         0.716       0.168       0.115       1
## Obs 73         0.651       0.089       0.260       1
## Obs 74         0.522       0.180       0.298       1
## Obs 75         0.768       0.121       0.110       1
## Obs 76         0.675       0.166       0.159       1
## Obs 77         0.689       0.109       0.202       1
## Obs 78         0.592       0.081       0.326       1
## Obs 79         0.821       0.054       0.126       1
## Obs 80         0.630       0.279       0.091       1
## Obs 81         0.672       0.199       0.129       1
## Obs 82         0.622       0.244       0.134       1
## Obs 83         0.841       0.098       0.060       1
## Obs 84         0.522       0.092       0.386       1
## Obs 85         0.452       0.188       0.361       1
## Obs 86         0.514       0.222       0.264       1
## Obs 87         0.731       0.112       0.157       1
## Obs 88         0.539       0.198       0.263       1
## Obs 89         0.664       0.185       0.151       1
## Obs 90         0.683       0.153       0.165       1
## Obs 91         0.489       0.211       0.300       1
## Obs 92         0.809       0.073       0.118       1
## Obs 93         0.836       0.091       0.073       1
## Obs 94         0.543       0.332       0.125       1
## Obs 95         0.773       0.099       0.128       1
## Obs 96         0.585       0.234       0.181       1
## Obs 97         0.762       0.118       0.120       1
## Obs 98         0.878       0.062       0.060       1
## Obs 99         0.483       0.386       0.130       1
## Obs 100        0.860       0.071       0.069       1
## Obs 101        0.164       0.102       0.734       3
## Obs 102        0.196       0.090       0.714       3
## Obs 103        0.285       0.075       0.640       3
## Obs 104        0.478       0.097       0.425       1
## Obs 105        0.128       0.054       0.818       3
## Obs 106        0.620       0.103       0.278       1
## Obs 107        0.314       0.204       0.481       3
## Obs 108        0.617       0.110       0.272       1
## Obs 109        0.554       0.128       0.318       1
## Obs 110        0.162       0.098       0.740       3
## Obs 111        0.145       0.067       0.788       3
## Obs 112        0.196       0.062       0.742       3
## Obs 113        0.074       0.033       0.893       3
## Obs 114        0.203       0.147       0.650       3
## Obs 115        0.127       0.116       0.757       3
## Obs 116        0.060       0.043       0.897       3
## Obs 117        0.533       0.060       0.407       1
## Obs 118        0.527       0.159       0.314       1
## Obs 119        0.501       0.188       0.311       1
## Obs 120        0.483       0.195       0.322       1
## Obs 121        0.061       0.035       0.904       3
## Obs 122        0.151       0.092       0.757       3
## Obs 123        0.616       0.124       0.260       1
## Obs 124        0.219       0.084       0.697       3
## Obs 125        0.212       0.066       0.721       3
## Obs 126        0.652       0.089       0.259       1
## Obs 127        0.186       0.072       0.741       3
## Obs 128        0.213       0.059       0.728       3
## Obs 129        0.141       0.062       0.797       3
## Obs 130        0.612       0.106       0.281       1
## Obs 131        0.604       0.099       0.297       1
## Obs 132        0.550       0.168       0.283       1
## Obs 133        0.112       0.065       0.823       3
## Obs 134        0.700       0.067       0.233       1
## Obs 135        0.395       0.222       0.384       1
## Obs 136        0.273       0.151       0.575       3
## Obs 137        0.118       0.076       0.806       3
## Obs 138        0.495       0.084       0.421       1
## Obs 139        0.218       0.073       0.709       3
## Obs 140        0.123       0.062       0.815       3
## Obs 141        0.057       0.043       0.899       3
## Obs 142        0.154       0.152       0.694       3
## Obs 143        0.196       0.090       0.714       3
## Obs 144        0.088       0.041       0.872       3
## Obs 145        0.067       0.051       0.883       3
## Obs 146        0.113       0.103       0.784       3
## Obs 147        0.232       0.149       0.619       3
## Obs 148        0.041       0.018       0.941       3
## Obs 149        0.132       0.083       0.785       3
## Obs 150        0.302       0.091       0.607       3
##
## Centroid:
##
##              Sepal.Length   Sepal.Width   Petal.Length   Petal.Width
## ----------  -------------  ------------  -------------  ------------
## Cluster 1           6.194         2.831          4.615         1.440
## Cluster 2           5.058         3.403          1.609         0.302
## Cluster 3           6.420         2.996          5.333         2.053

## Visualization

For visualization this package provide biplot and radar plot

### Biplot

Biplot perform visualization with Principal Component Analysis. Use scale =T when unit of variables on data are different.

biploting(cl_CM, iris[,1:4], scale=T)->biplot

Radar plot can be used to profilling your cluster result via centroid. Please take attention to axis label. 0 indicates mean of variable, 0.5 indicates mean plus half of standar deviation in realted variable, -0.5 indicates mean minus half of standar deviation in related variable, etc.

radar.plotting(cl_CM, iris[,1:4])->radar
## Using Cluster as id variables

## Validation

To get best parameter and know how well your result, use validation index that provided. There are Xie Beni, Partition Coefficient, Modified Partition Coefficient, Classification Entropy, Kwon, Tang, and Separation. See details in ?validation.index

validation.index(cl_GK)
## Validation Index result:
##
##                                    Value
## -------------------------------  -------
## Partition Coefficient              0.728
## Modified Partition Coefficient     0.592
## Classification Entropy             0.466
## Xie Beni                           0.189
## Separation                         0.189
## Kwon                              48.454
## Tang                              38.430

## Consensus Clustering

Combine several fuzzy cluster result, eg: FCM, GK, GG, to one result. The purpose of this action is to get best stable or robust result. Actually when you run 3 times, with no specific random number, the first result may be different with second time. And choosing best random number is hard to describe. So the alternative is you can combine your result with consensus algorithm.

Right now, this package provide VOTING method. This method inspired from domination in voting schema. Algorithm that use in this package are “sum”, “product”, “borda”. “product” is sensitive when there is low membership on your result.

c_fuzzycluster(cl_GK,cl_GG,cl_CM)->c_consensus
co.vote(c_consensus,"sum")
## Method of Consensus used:    Vote-sum
## Ensemble/Consensus Membership:
##
##            Cluster 1   Cluster 2   Cluster 3
## --------  ----------  ----------  ----------
## Obs 1          0.003       0.995       0.001
## Obs 2          0.032       0.957       0.010
## Obs 3          0.015       0.979       0.005
## Obs 4          0.027       0.963       0.010
## Obs 5          0.005       0.993       0.002
## Obs 6          0.032       0.954       0.013
## Obs 7          0.036       0.952       0.012
## Obs 8          0.003       0.996       0.001
## Obs 9          0.057       0.924       0.019
## Obs 10         0.033       0.955       0.012
## Obs 11         0.019       0.973       0.008
## Obs 12         0.019       0.974       0.007
## Obs 13         0.036       0.951       0.013
## Obs 14         0.064       0.913       0.023
## Obs 15         0.060       0.913       0.027
## Obs 16         0.067       0.902       0.031
## Obs 17         0.044       0.939       0.017
## Obs 18         0.007       0.991       0.002
## Obs 19         0.047       0.933       0.020
## Obs 20         0.016       0.977       0.006
## Obs 21         0.040       0.945       0.015
## Obs 22         0.023       0.968       0.008
## Obs 23         0.051       0.930       0.019
## Obs 24         0.052       0.932       0.016
## Obs 25         0.064       0.908       0.028
## Obs 26         0.042       0.944       0.014
## Obs 27         0.017       0.977       0.006
## Obs 28         0.008       0.990       0.003
## Obs 29         0.012       0.984       0.004
## Obs 30         0.025       0.966       0.009
## Obs 31         0.023       0.969       0.008
## Obs 32         0.045       0.940       0.015
## Obs 33         0.046       0.933       0.021
## Obs 34         0.042       0.939       0.019
## Obs 35         0.017       0.977       0.006
## Obs 36         0.029       0.961       0.009
## Obs 37         0.043       0.941       0.016
## Obs 38         0.018       0.974       0.007
## Obs 39         0.051       0.932       0.017
## Obs 40         0.005       0.993       0.002
## Obs 41         0.014       0.981       0.005
## Obs 42         0.204       0.738       0.058
## Obs 43         0.048       0.936       0.017
## Obs 44         0.093       0.878       0.029
## Obs 45         0.052       0.928       0.021
## Obs 46         0.039       0.950       0.011
## Obs 47         0.023       0.967       0.010
## Obs 48         0.021       0.971       0.008
## Obs 49         0.013       0.981       0.005
## Obs 50         0.005       0.993       0.002
## Obs 51         0.598       0.089       0.314
## Obs 52         0.750       0.064       0.186
## Obs 53         0.621       0.051       0.328
## Obs 54         0.706       0.100       0.194
## Obs 55         0.738       0.046       0.217
## Obs 56         0.731       0.061       0.209
## Obs 57         0.661       0.066       0.273
## Obs 58         0.635       0.220       0.145
## Obs 59         0.748       0.053       0.198
## Obs 60         0.649       0.103       0.248
## Obs 61         0.585       0.219       0.196
## Obs 62         0.760       0.064       0.176
## Obs 63         0.668       0.118       0.214
## Obs 64         0.835       0.028       0.138
## Obs 65         0.714       0.140       0.145
## Obs 66         0.690       0.091       0.219
## Obs 67         0.667       0.064       0.269
## Obs 68         0.698       0.108       0.194
## Obs 69         0.594       0.103       0.302
## Obs 70         0.816       0.078       0.107
## Obs 71         0.456       0.057       0.487
## Obs 72         0.830       0.068       0.101
## Obs 73         0.677       0.041       0.282
## Obs 74         0.664       0.073       0.263
## Obs 75         0.832       0.053       0.116
## Obs 76         0.737       0.073       0.190
## Obs 77         0.652       0.053       0.296
## Obs 78         0.499       0.037       0.464
## Obs 79         0.869       0.021       0.110
## Obs 80         0.744       0.148       0.108
## Obs 81         0.781       0.099       0.120
## Obs 82         0.740       0.126       0.134
## Obs 83         0.897       0.046       0.057
## Obs 84         0.554       0.042       0.404
## Obs 85         0.607       0.081       0.312
## Obs 86         0.636       0.096       0.268
## Obs 87         0.696       0.053       0.252
## Obs 88         0.683       0.085       0.232
## Obs 89         0.782       0.077       0.141
## Obs 90         0.793       0.068       0.138
## Obs 91         0.660       0.086       0.254
## Obs 92         0.852       0.031       0.117
## Obs 93         0.900       0.040       0.060
## Obs 94         0.642       0.217       0.141
## Obs 95         0.854       0.040       0.106
## Obs 96         0.741       0.094       0.165
## Obs 97         0.850       0.047       0.103
## Obs 98         0.915       0.026       0.059
## Obs 99         0.569       0.279       0.152
## Obs 100        0.910       0.030       0.060
## Obs 101        0.150       0.047       0.804
## Obs 102        0.330       0.043       0.626
## Obs 103        0.188       0.029       0.782
## Obs 104        0.353       0.040       0.607
## Obs 105        0.091       0.022       0.887
## Obs 106        0.458       0.050       0.492
## Obs 107        0.474       0.107       0.419
## Obs 108        0.450       0.049       0.501
## Obs 109        0.407       0.052       0.541
## Obs 110        0.150       0.046       0.804
## Obs 111        0.164       0.031       0.805
## Obs 112        0.193       0.028       0.779
## Obs 113        0.051       0.013       0.937
## Obs 114        0.357       0.068       0.575
## Obs 115        0.239       0.060       0.701
## Obs 116        0.086       0.022       0.892
## Obs 117        0.355       0.024       0.621
## Obs 118        0.439       0.077       0.484
## Obs 119        0.405       0.087       0.508
## Obs 120        0.585       0.083       0.332
## Obs 121        0.050       0.015       0.936
## Obs 122        0.334       0.047       0.620
## Obs 123        0.470       0.061       0.469
## Obs 124        0.341       0.039       0.621
## Obs 125        0.144       0.026       0.830
## Obs 126        0.463       0.038       0.499
## Obs 127        0.354       0.034       0.613
## Obs 128        0.340       0.029       0.631
## Obs 129        0.113       0.025       0.861
## Obs 130        0.444       0.045       0.510
## Obs 131        0.433       0.044       0.523
## Obs 132        0.461       0.081       0.458
## Obs 133        0.099       0.027       0.874
## Obs 134        0.638       0.033       0.329
## Obs 135        0.411       0.097       0.492
## Obs 136        0.229       0.067       0.705
## Obs 137        0.122       0.036       0.842
## Obs 138        0.354       0.034       0.612
## Obs 139        0.381       0.034       0.585
## Obs 140        0.092       0.024       0.884
## Obs 141        0.051       0.018       0.930
## Obs 142        0.151       0.066       0.784
## Obs 143        0.330       0.043       0.626
## Obs 144        0.068       0.017       0.915
## Obs 145        0.067       0.023       0.910
## Obs 146        0.112       0.044       0.844
## Obs 147        0.328       0.064       0.608
## Obs 148        0.078       0.011       0.911
## Obs 149        0.151       0.040       0.809
## Obs 150        0.383       0.043       0.574
##
## Ensemble/Consensus Label:
##
##            label
## --------  ------
## Obs 1          2
## Obs 2          2
## Obs 3          2
## Obs 4          2
## Obs 5          2
## Obs 6          2
## Obs 7          2
## Obs 8          2
## Obs 9          2
## Obs 10         2
## Obs 11         2
## Obs 12         2
## Obs 13         2
## Obs 14         2
## Obs 15         2
## Obs 16         2
## Obs 17         2
## Obs 18         2
## Obs 19         2
## Obs 20         2
## Obs 21         2
## Obs 22         2
## Obs 23         2
## Obs 24         2
## Obs 25         2
## Obs 26         2
## Obs 27         2
## Obs 28         2
## Obs 29         2
## Obs 30         2
## Obs 31         2
## Obs 32         2
## Obs 33         2
## Obs 34         2
## Obs 35         2
## Obs 36         2
## Obs 37         2
## Obs 38         2
## Obs 39         2
## Obs 40         2
## Obs 41         2
## Obs 42         2
## Obs 43         2
## Obs 44         2
## Obs 45         2
## Obs 46         2
## Obs 47         2
## Obs 48         2
## Obs 49         2
## Obs 50         2
## Obs 51         1
## Obs 52         1
## Obs 53         1
## Obs 54         1
## Obs 55         1
## Obs 56         1
## Obs 57         1
## Obs 58         1
## Obs 59         1
## Obs 60         1
## Obs 61         1
## Obs 62         1
## Obs 63         1
## Obs 64         1
## Obs 65         1
## Obs 66         1
## Obs 67         1
## Obs 68         1
## Obs 69         1
## Obs 70         1
## Obs 71         3
## Obs 72         1
## Obs 73         1
## Obs 74         1
## Obs 75         1
## Obs 76         1
## Obs 77         1
## Obs 78         1
## Obs 79         1
## Obs 80         1
## Obs 81         1
## Obs 82         1
## Obs 83         1
## Obs 84         1
## Obs 85         1
## Obs 86         1
## Obs 87         1
## Obs 88         1
## Obs 89         1
## Obs 90         1
## Obs 91         1
## Obs 92         1
## Obs 93         1
## Obs 94         1
## Obs 95         1
## Obs 96         1
## Obs 97         1
## Obs 98         1
## Obs 99         1
## Obs 100        1
## Obs 101        3
## Obs 102        3
## Obs 103        3
## Obs 104        3
## Obs 105        3
## Obs 106        3
## Obs 107        1
## Obs 108        3
## Obs 109        3
## Obs 110        3
## Obs 111        3
## Obs 112        3
## Obs 113        3
## Obs 114        3
## Obs 115        3
## Obs 116        3
## Obs 117        3
## Obs 118        3
## Obs 119        3
## Obs 120        1
## Obs 121        3
## Obs 122        3
## Obs 123        1
## Obs 124        3
## Obs 125        3
## Obs 126        3
## Obs 127        3
## Obs 128        3
## Obs 129        3
## Obs 130        3
## Obs 131        3
## Obs 132        1
## Obs 133        3
## Obs 134        1
## Obs 135        3
## Obs 136        3
## Obs 137        3
## Obs 138        3
## Obs 139        3
## Obs 140        3
## Obs 141        3
## Obs 142        3
## Obs 143        3
## Obs 144        3
## Obs 145        3
## Obs 146        3
## Obs 147        3
## Obs 148        3
## Obs 149        3
## Obs 150        3