Rough-Fuzzy Pattern Recognition

Foreword xiii
Preface xv
About the Authors xix
1 Introduction to Pattern Recognition and Data Mining1
1.1 Introduction, 1
1.2 Pattern Recognition, 3
1.3 Data Mining, 6
1.4 Relevance of Soft Computing, 9
1.5 Scope and Organization of the Book, 10
2 Rough-Fuzzy Hybridization and Granular Computing 21
2.1 Introduction, 21
2.2 Fuzzy Sets, 22
2.3 Rough Sets, 23
2.4 Emergence of Rough-Fuzzy Computing, 26
2.5 Generalized Rough Sets, 29
2.6 Entropy Measures, 30
2.7 Conclusion and Discussion, 36
3 Rough-Fuzzy Clustering: Generalized c-MeansAlgorithm 47
3.1 Introduction, 47
3.2 Existing c-Means Algorithms, 49
3.4 Generalization of Existing c-Means Algorithms, 61
3.5 Quantitative Indices for Rough-Fuzzy Clustering, 65
3.6 Performance Analysis, 68
3.7 Conclusion and Discussion, 80
4 Rough-Fuzzy Granulation and Pattern Classification85
4.1 Introduction, 85
4.2 Pattern Classification Model, 87
4.3 Quantitative Measures, 95
4.4 Description of Data Sets, 97
4.5 Experimental Results, 100
4.6 Conclusion and Discussion, 112
5 Fuzzy-Rough Feature Selection using f -InformationMeasures 117
5.1 Introduction, 117
5.2 Fuzzy-Rough Sets, 120
5.3 Information Measure on Fuzzy Approximation Spaces, 121
5.4 f -Information and Fuzzy Approximation Spaces,125
5.5 f -Information for Feature Selection, 129
5.6 Quantitative Measures, 133
5.7 Experimental Results, 135
5.8 Conclusion and Discussion, 156
6 Rough Fuzzy c-Medoids and Amino Acid SequenceAnalysis 161
6.1 Introduction, 161
6.2 Bio-Basis Function and String Selection Methods, 164
6.3 Fuzzy-Possibilistic c-Medoids Algorithm, 168
6.4 Rough-Fuzzy c-Medoids Algorithm, 172
6.5 Relational Clustering for Bio-Basis String Selection,176
6.6 Quantitative Measures, 178
6.7 Experimental Results, 181
6.8 Conclusion and Discussion, 196
7 Clustering Functionally Similar Genes from Microarray Data201
7.1 Introduction, 201
7.2 Clustering Gene Expression Data, 203
7.3 Quantitative and Qualitative Analysis, 207
7.4 Description of Data Sets, 209
7.5 Experimental Results, 212
7.6 Conclusion and Discussion, 217
8 Selection of Discriminative Genes from Microarray Data225
8.1 Introduction, 225
8.2 Evaluation Criteria for Gene Selection, 227
8.3 Approximation of Density Function, 230
8.4 Gene Selection using Information Measures, 234
8.5 Experimental Results, 235
8.6 Conclusion and Discussion, 250
9 Segmentation of Brain Magnetic Resonance Images 257
9.1 Introduction, 257
9.2 Pixel Classification of Brain MR Images, 259
9.3 Segmentation of Brain MR Images, 264
9.4 Experimental Results, 277
9.5 Conclusion and Discussion, 283
References, 283
Index 287