Rough-Fuzzy Pattern Recognition (eBook)

PRADIPTA MAJI, PHD, is Assistant Professor in the Machine Intelligence Unit of the Indian Statistical Institute. His research explores pattern recognition, bioinformatics, medical image processing, cellular automata, and soft computing. SANKAR K. PAL, PHD, is Director and Distinguished Scientist of the Indian Statistical Institute. He is also a J. C. Bose Fellow of the Government of India. Dr. Pal founded both the Machine Intelligence Unit and the Center for Soft Computing Research at the Indian Statistical Institute. He is a Fellow of the IEEE, IAPR, IFSA, TWAS, and Indian National Science Academy.

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