Knowledge-Based Clustering: From Data to Information Granules

Cover......Page 1
Contents......Page 10
Foreword......Page 16
Preface......Page 18
1.2. BASIC NOTIONS AND NOTATION......Page 22
1.2.2. Distance and Similarity......Page 23
1.3.1. Hierarchical Clustering......Page 27
1.3.2. Objective Function-Based Clustering......Page 29
1.4. CLUSTERING AND CLASSIFICATION......Page 31
1.5. FUZZY CLUSTERING......Page 32
1.6. CLUSTER VALIDITY......Page 39
1.7.1. Augmented Geometry of Fuzzy Clusters: Fuzzy C Varieties......Page 40
1.7.2. Possibilistic Clustering......Page 41
1.7.3. Noise Clustering......Page 43
1.8. SELF-ORGANIZING MAPS AND FUZZY OBJECTIVE......Page 44
1.9. CONCLUSIONS......Page 46
3.1. INTRODUCTION......Page 71
3.2. MAIN CATEGORIES OF FUZZY NEURONS......Page 72
3.2.1. Aggregative Neurons......Page 73
3.2.2. Referential (Reference) Neurons......Page 76
3.3. ARCHITECTURES OF LOGIC NETWORKS......Page 80
3.4. INTERPRETATION ASPECTS OF THE NETWORKS......Page 82
3.5. GRANULAR INTERFACES OF LOGIC PROCESSING......Page 83
3.6. CONCLUSIONS......Page 85
4.1. INTRODUCTION......Page 87
4.2. PROBLEM STATEMENT: CONTEXT FUZZY SETS......Page 89
4.3. THE OPTIMIZATION PROBLEM......Page 91
4.4. COMPUTATIONAL CONSIDERATIONS......Page 101
4.5. GENERALIZATIONS OF THE ALGORITHM THROUGH......Page 102
4.6. FUZZY CLUSTERING WITH SPATIAL CONSTRAINTS......Page 103
4.7. CONCLUSIONS......Page 107
6.1. INTRODUCTION......Page 118
6.2. EXAMPLES OF KNOWLEDGE-ORIENTED HINTS......Page 120
6.3. THE OPTIMIZATION ENVIRONMENT......Page 123
6.4. QUANTIFICATION OF KNOWLEDGE-BASED GUIDANCE HINTS......Page 126
6.5. ORGANIZATION OF THE INTERACTION PROCESS......Page 128
6.6. PROXIMITY-BASED CLUSTERING (P-FCM)......Page 133
6.7. WEB EXPLORATION AND P-FCM......Page 138
6.8. LINGUISTIC AUGMENTATION OF KNOWLEDGE-BASED HINTS......Page 147
6.9. CONCLUSIONS......Page 148
7.1. INTRODUCTION AND RATIONALE......Page 150
7.2. HORIZONTAL AND VERTICAL CLUSTERING......Page 152
7.3. HORIZONTAL COLLABORATIVE CLUSTERING......Page 153
7.3.1. Optimization Details......Page 156
7.3.2. The Flow of Computing of Collaborative Clustering......Page 158
7.3.3. Quantification of the Collaborative Phenomenon of Clustering......Page 159
7.4. EXPERIMENTAL STUDIES......Page 161
7.5. FURTHER ENHANCEMENTS OF HORIZONTAL CLUSTERING......Page 171
7.6. THE ALGORITHM OF VERTICAL CLUSTERING......Page 172
7.7. A GRID MODEL OF HORIZONTAL AND VERTICAL......Page 174
7.8. CONSENSUS CLUSTERING......Page 176
7.9. CONCLUSIONS......Page 178
8.1. INTRODUCTION......Page 179
8.2. PROBLEM FORMULATION......Page 180
8.2.1. The Objective Function......Page 181
8.2.2. The Logic Transformation Between Information Granules......Page 182
8.3. THE ALGORITHM......Page 184
8.4. THE DEVELOPMENT FRAMEWORK......Page 187
8.5. NUMERICAL STUDIES......Page 188
8.6. CONCLUSIONS......Page 195
9.1. INTRODUCTION AND PROBLEM STATEMENT......Page 199
9.2. FCM FOR RELATIONAL DATA......Page 200
9.3. DECOMPOSITION OF FUZZY RELATIONAL PATTERNS......Page 202
9.3.1. Gradient-Based Solution to the Decomposition Problem......Page 203
9.3.2. Neural Network Model of the Decomposition Problem......Page 205
9.4. COMPARATIVE ANALYSIS......Page 209
9.5. CONCLUSIONS......Page 210
10.1. INTRODUCTION......Page 212
10.2. HETEROGENEOUS DATA......Page 213
10.3. PARAMETRIC MODELS OF GRANULAR DATA......Page 215
10.4. PARAMETRIC MODE OF HETEROGENEOUS......Page 216
10.5.1. A Frame of Reference......Page 219
10.5.2. Representation of Granular Data Through the Possibility-Necessity......Page 221
10.5.3. Dereferencing......Page 226
10.6. CONCLUSIONS......Page 228
11.1. INTRODUCTION......Page 230
11.2. PROBLEM FORMULATION......Page 231
11.3. THE CLUSTERING ALGORITHM—DETAILED......Page 232
11.4. DEVELOPMENT OF GRANULAR PROTOTYPES......Page 239
11.5. GEOMETRY OF INFORMATION GRANULES......Page 241
11.7. CONCLUSIONS......Page 244
12.1. INTRODUCTION......Page 247
12.2. OPERATIONS OF THRESHOLDING AND TOLERANCE:......Page 248
12.3. TOPOLOGY OF THE LOGIC NETWORK......Page 252
12.4. GENETIC OPTIMIZATION......Page 256
12.5. ILLUSTRATIVE NUMERIC STUDIES......Page 257
12.6. CONCLUSIONS......Page 265
13.1. INTRODUCTION......Page 267
13.2.1. Expressing Similarity Between Two Fuzzy Sets......Page 268
13.2.2. Performance Index (Objective Function)......Page 269
13.3. PROTOTYPE OPTIMIZATION......Page 272
13.4.1. Optimization of the Similarity Levels......Page 284
13.4.2. An Inverse Similarity Problem......Page 285
13.5. CONCLUSIONS......Page 289
14.1. INTRODUCTION AND PROBLEM STATEMENT......Page 291
14.2. POSSIBILITY AND NECESSITY MEASURES AS THE......Page 292
14.3. BUILDING THE GRANULAR MAPPING......Page 293
14.4. DESIGNING MULTIVARIABLE GRANULAR MAPPINGS......Page 296
14.6. EXPERIMENTAL STUDIES......Page 299
14.7. CONCLUSIONS......Page 301
15.1. INTRODUCTION......Page 304
15.2. CLUSTER-BASED REPRESENTATION......Page 306
15.3. CONDITIONAL CLUSTERING IN THE DEVELOPMENT......Page 308
15.4. THE GRANULAR NEURON AS A GENERIC PROCESSING......Page 311
15.5. THE ARCHITECTURE OF LINGUISTIC MODELS BASED......Page 314
15.6. REFINEMENTS OF LINGUISTIC MODELS......Page 315
15.7. CONCLUSIONS......Page 316
Bibliography......Page 318
Index......Page 336