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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

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

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

wsrd43

0.404

0.494

0.248

0.341

0.694

0.428

wsrd44

0.504

0.616

0.279

0.616

0.849

0.617

wsrd45

0.58

0.948

0.304

0.418

0.636

0.295

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

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

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

 

*          Contact

Mohamed[DOT]Sellami[AT]it-sudparis.eu

 

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