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Fuzzy C-means clustering of Web service registries
Fuzzy C-means clustering of Web service registries
Abstract
To ease the registry discovery
step in a Web services discovery process, we propose to group Web service
registries according to the functionalities of the services they advertise.
We characterize each Web services registry with a semantic description. This
description, that we call Web Services Registry Description (WSRD),
represents the signature of a Web services registry and is mainly based on
the service signatures advertised in the registry. We then employ these
descriptions to ensure functionality-driven clustering of Web service
registries.
In this document, we present
details on the experiments of our fuzzy clustering technique using the Fuzzy Clustering and
Data Analysis Toolbox.
The used data
To simulate a fuzzy
clustering of a set of registries using the fuzzy C-means technique, we first
create a set of WSRD descriptions for the registries using our WSRD generator.
We generated 100 WSRD descriptions and transformed them into 6-dimensional
vectors according to our proposed vector space. The table below illustrates
the 100 representative vectors of our WSRD description set.
|
|
w1
|
w2
|
w3
|
w4
|
w5
|
w6
|
|
wsrd1
|
0.234
|
0.314
|
0.048
|
0.181
|
0.534
|
0.268
|
|
wsrd2
|
0.334
|
0.426
|
0.099
|
0.456
|
0.689
|
0.457
|
|
wsrd3
|
0.5
|
0.758
|
0.124
|
0.258
|
0.456
|
0.125
|
|
wsrd4
|
0.6
|
0.209
|
0.126
|
0.135
|
0.214
|
0.145
|
|
wsrd5
|
0.2
|
0.522
|
0.127
|
0.145
|
0.785
|
0.456
|
|
wsrd6
|
0.1
|
0.365
|
0.356
|
0.189
|
0.369
|
0.741
|
|
wsrd7
|
0.254
|
0.344
|
0.098
|
0.191
|
0.544
|
0.278
|
|
wsrd8
|
0.354
|
0.466
|
0.109
|
0.466
|
0.699
|
0.467
|
|
wsrd9
|
0.4
|
0.788
|
0.134
|
0.268
|
0.466
|
0.135
|
|
wsrd10
|
0.5
|
0.219
|
0.136
|
0.145
|
0.224
|
0.155
|
|
wsrd11
|
0.25
|
0.512
|
0.137
|
0.155
|
0.795
|
0.466
|
|
wsrd12
|
0.15
|
0.369
|
0.366
|
0.199
|
0.379
|
0.751
|
|
wsrd13
|
0.274
|
0.364
|
0.118
|
0.211
|
0.564
|
0.298
|
|
wsrd14
|
0.374
|
0.486
|
0.129
|
0.486
|
0.719
|
0.487
|
|
wsrd15
|
0.45
|
0.808
|
0.154
|
0.288
|
0.486
|
0.155
|
|
wsrd16
|
0.55
|
0.239
|
0.156
|
0.165
|
0.244
|
0.175
|
|
wsrd17
|
0.27
|
0.532
|
0.157
|
0.175
|
0.815
|
0.486
|
|
wsrd18
|
0.17
|
0.371
|
0.386
|
0.219
|
0.399
|
0.771
|
|
wsrd19
|
0.294
|
0.384
|
0.138
|
0.231
|
0.584
|
0.318
|
|
wsrd20
|
0.394
|
0.506
|
0.149
|
0.506
|
0.739
|
0.507
|
|
wsrd21
|
0.47
|
0.838
|
0.174
|
0.308
|
0.506
|
0.175
|
|
wsrd22
|
0.57
|
0.259
|
0.176
|
0.185
|
0.264
|
0.195
|
|
wsrd23
|
0.29
|
0.552
|
0.177
|
0.195
|
0.835
|
0.506
|
|
wsrd24
|
0.19
|
0.391
|
0.406
|
0.239
|
0.419
|
0.791
|
|
wsrd25
|
0.314
|
0.404
|
0.158
|
0.251
|
0.604
|
0.338
|
|
wsrd26
|
0.414
|
0.526
|
0.169
|
0.526
|
0.759
|
0.527
|
|
wsrd27
|
0.49
|
0.858
|
0.194
|
0.328
|
0.526
|
0.195
|
|
wsrd28
|
0.59
|
0.279
|
0.196
|
0.205
|
0.284
|
0.215
|
|
wsrd29
|
0.31
|
0.572
|
0.197
|
0.215
|
0.855
|
0.526
|
|
wsrd30
|
0.22
|
0.411
|
0.426
|
0.259
|
0.439
|
0.811
|
|
wsrd31
|
0.334
|
0.424
|
0.178
|
0.271
|
0.624
|
0.358
|
|
wsrd32
|
0.434
|
0.546
|
0.199
|
0.546
|
0.779
|
0.547
|
|
wsrd33
|
0.51
|
0.878
|
0.224
|
0.348
|
0.546
|
0.225
|
|
wsrd34
|
0.61
|
0.299
|
0.226
|
0.225
|
0.304
|
0.235
|
|
wsrd35
|
0.33
|
0.592
|
0.227
|
0.235
|
0.875
|
0.556
|
|
wsrd36
|
0.25
|
0.431
|
0.446
|
0.279
|
0.459
|
0.831
|
|
wsrd37
|
0.354
|
0.444
|
0.198
|
0.291
|
0.644
|
0.378
|
|
wsrd38
|
0.454
|
0.566
|
0.229
|
0.566
|
0.799
|
0.567
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|
wsrd39
|
0.53
|
0.898
|
0.254
|
0.368
|
0.586
|
0.245
|
|
wsrd40
|
0.63
|
0.319
|
0.246
|
0.275
|
0.324
|
0.255
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|
wsrd41
|
0.35
|
0.612
|
0.247
|
0.255
|
0.895
|
0.576
|
|
wsrd42
|
0.27
|
0.451
|
0.466
|
0.299
|
0.479
|
0.851
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|
wsrd43
|
0.404
|
0.494
|
0.248
|
0.341
|
0.694
|
0.428
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|
wsrd44
|
0.504
|
0.616
|
0.279
|
0.616
|
0.849
|
0.617
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|
wsrd45
|
0.58
|
0.948
|
0.304
|
0.418
|
0.636
|
0.295
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|
wsrd46
|
0.68
|
0.369
|
0.296
|
0.325
|
0.374
|
0.305
|
|
wsrd47
|
0.4
|
0.662
|
0.297
|
0.305
|
0.945
|
0.626
|
|
wsrd48
|
0.32
|
0.501
|
0.516
|
0.349
|
0.529
|
0.901
|
|
wsrd49
|
0.454
|
0.544
|
0.298
|
0.391
|
0.744
|
0.478
|
|
wsrd50
|
0.554
|
0.666
|
0.329
|
0.666
|
0.899
|
0.667
|
|
wsrd51
|
0.63
|
0.998
|
0.354
|
0.468
|
0.686
|
0.345
|
|
wsrd52
|
0.73
|
0.419
|
0.346
|
0.375
|
0.424
|
0.355
|
|
wsrd53
|
0.45
|
0.712
|
0.347
|
0.355
|
0.995
|
0.676
|
|
wsrd54
|
0.37
|
0.551
|
0.566
|
0.399
|
0.579
|
0.951
|
|
wsrd55
|
0.504
|
0.594
|
0.348
|
0.411
|
0.794
|
0.528
|
|
wsrd56
|
0.604
|
0.716
|
0.379
|
0.716
|
0.949
|
0.717
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|
wsrd57
|
0.68
|
0.048
|
0.404
|
0.518
|
0.736
|
0.395
|
|
wsrd58
|
0.78
|
0.469
|
0.396
|
0.425
|
0.474
|
0.405
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|
wsrd59
|
0.5
|
0.762
|
0.397
|
0.405
|
0.045
|
0.726
|
|
wsrd60
|
0.42
|
0.601
|
0.616
|
0.449
|
0.629
|
0.001
|
|
wsrd61
|
0.554
|
0.644
|
0.398
|
0.461
|
0.844
|
0.578
|
|
wsrd62
|
0.654
|
0.766
|
0.429
|
0.766
|
0.999
|
0.767
|
|
wsrd63
|
0.73
|
0.098
|
0.454
|
0.568
|
0.786
|
0.445
|
|
wsrd64
|
0.83
|
0.519
|
0.446
|
0.475
|
0.524
|
0.475
|
|
wsrd65
|
0.55
|
0.812
|
0.447
|
0.455
|
0.095
|
0.776
|
|
wsrd66
|
0.47
|
0.651
|
0.666
|
0.499
|
0.679
|
0.051
|
|
wsrd67
|
0.604
|
0.694
|
0.448
|
0.511
|
0.894
|
0.628
|
|
wsrd68
|
0.704
|
0.816
|
0.479
|
0.816
|
0.049
|
0.817
|
|
wsrd69
|
0.78
|
0.148
|
0.504
|
0.618
|
0.836
|
0.495
|
|
wsrd70
|
0.88
|
0.569
|
0.496
|
0.525
|
0.574
|
0.525
|
|
wsrd71
|
0.6
|
0.862
|
0.497
|
0.505
|
0.145
|
0.826
|
|
wsrd72
|
0.52
|
0.701
|
0.716
|
0.549
|
0.729
|
0.101
|
|
wsrd73
|
0.654
|
0.744
|
0.498
|
0.561
|
0.944
|
0.678
|
|
wsrd74
|
0.754
|
0.866
|
0.529
|
0.866
|
0.099
|
0.867
|
|
wsrd75
|
0.83
|
0.198
|
0.554
|
0.668
|
0.886
|
0.545
|
|
wsrd76
|
0.93
|
0.619
|
0.546
|
0.575
|
0.624
|
0.575
|
|
wsrd77
|
0.65
|
0.912
|
0.547
|
0.555
|
0.195
|
0.876
|
|
wsrd78
|
0.57
|
0.751
|
0.766
|
0.599
|
0.779
|
0.151
|
|
wsrd79
|
0.704
|
0.794
|
0.548
|
0.611
|
0.994
|
0.728
|
|
wsrd80
|
0.804
|
0.916
|
0.579
|
0.916
|
0.149
|
0.917
|
|
wsrd81
|
0.88
|
0.248
|
0.604
|
0.718
|
0.936
|
0.595
|
|
wsrd82
|
0.98
|
0.669
|
0.596
|
0.625
|
0.674
|
0.625
|
|
wsrd83
|
0.70
|
0.962
|
0.597
|
0.645
|
0.245
|
0.926
|
|
wsrd84
|
0.62
|
0.801
|
0.816
|
0.649
|
0.829
|
0.201
|
|
wsrd85
|
0.754
|
0.844
|
0.598
|
0.661
|
0.044
|
0.778
|
|
wsrd86
|
0.854
|
0.966
|
0.629
|
0.966
|
0.199
|
0.967
|
|
wsrd87
|
0.93
|
0.298
|
0.654
|
0.768
|
0.986
|
0.645
|
|
wsrd88
|
0.03
|
0.719
|
0.646
|
0.675
|
0.724
|
0.675
|
|
wsrd89
|
0.75
|
0.012
|
0.647
|
0.695
|
0.295
|
0.976
|
|
wsrd90
|
0.67
|
0.851
|
0.866
|
0.699
|
0.879
|
0.251
|
|
wsrd91
|
0.804
|
0.894
|
0.648
|
0.711
|
0.094
|
0.828
|
|
wsrd92
|
0.904
|
0.016
|
0.679
|
0.016
|
0.249
|
0.017
|
|
wsrd93
|
0.98
|
0.348
|
0.704
|
0.818
|
0.036
|
0.695
|
|
wsrd94
|
0.08
|
0.769
|
0.696
|
0.725
|
0.774
|
0.725
|
|
wsrd95
|
0.80
|
0.062
|
0.697
|
0.745
|
0.345
|
0.026
|
|
wsrd96
|
0.72
|
0.901
|
0.916
|
0.749
|
0.929
|
0.301
|
|
wsrd97
|
0.854
|
0.944
|
0.698
|
0.761
|
0.144
|
0.878
|
|
wsrd98
|
0.954
|
0.066
|
0.729
|
0.066
|
0.299
|
0.067
|
|
wsrd99
|
0.03
|
0.398
|
0.754
|
0.868
|
0.086
|
0.745
|
|
wsrd100
|
0.62
|
0.801
|
0.816
|
0.649
|
0.829
|
0.201
|
Clustering results
We applied the fuzzy C-means
algorithm on our data set, using 2
as fuzzyness coefficient and 5 clusters. Since we can only graphically visualize our results
in 3 or 2 dimensional graphs, the 6 dimensions are devised in three
2-dimensions graphs (Fig. 1(a), Fig. 1(b) and Fig. 1(c)) and in two
3-dimensions graphs (Fig. 2(a) and Fig. 2(b)).
The two
dimensional graphs
Fig.
1(a). Axis XY represent the weights of w1 and w2 in a registry’s vector
Fig.
1(b). Axis XY represent the weights of w3 and w4 in a registry’s vector
Fig. 1(c). Axis XY represent
the weights of w5 and w6 in a registry’s vector
The
three dimensional graphs
Fig. 2(a). Axis XYZ
represent the weights of w1, w2 and w3 in a registry’s vector
Fig. 2(a). Axis XYZ
represent the weights of w4, w5 and w6 in a registry’s vector
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