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Emphasizing applications in bioinformatics and medical image processing, this text offers a clear framework that enables readers to take advantage of the latest rough-fuzzy computing techniques to build working pattern recognition models. The authors explain step by step how to integrate rough sets with fuzzy sets in order to best manage the uncertainties in mining large data sets. Chapters are logically organized according to the major phases of pattern recognition systems development, making it easier to master such tasks as classification, clustering, and feature selection.
Rough-Fuzzy Pattern Recognition examines the important underlying theory as well as algorithms and applications, helping readers see the connections between theory and practice. The first chapter provides an introduction to pattern recognition and data mining, including the key challenges of working with high-dimensional, real-life data sets. Next, the authors explore such topics and issues as:
Soft computing in pattern recognition and data mining
A Mathematical framework for generalized rough sets, incorporating the concept of fuzziness in defining the granules as well as the set
Selection of non-redundant and relevant features of real-valued data sets
Selection of the minimum set of basis strings with maximum information for amino acid sequence analysis
Segmentation of brain MR images for visualization of human tissues
Numerous examples and case studies help readers better understand how pattern recognition models are developed and used in practice. This text—covering the latest findings as well as directions for future research—is recommended for both students and practitioners working in systems design, pattern recognition, image analysis, data mining, bioinformatics, soft computing, and computational intelligence.
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.
Preface xv
About the Authors xix
1 Introduction to Pattern Recognition and Data Mining 1
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-Means Algorithm 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 Classification 85
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 -Information Measures 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 Sequence Analysis 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 Data 201
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 Data 225
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
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