Foreword | p. xiii |
Preface | p. xv |
About the Authors | p. xix |
Introduction to Pattern Recognition and Data Mining | p. 1 |
Introduction | p. 1 |
Pattern Recognition | p. 3 |
Data Acquisition | p. 4 |
Feature Selection | p. 4 |
Classification and Clustering | p. 5 |
Data Mining | p. 6 |
Tasks, Tools, and Applications | p. 7 |
Pattern Recognition Perspective | p. 8 |
Relevance of Soft Computing | p. 9 |
Scope and Organization of the Book | p. 10 |
References | p. 14 |
Rough-Fuzzy Hybridization and Granular Computing | p. 21 |
Introduction | p. 21 |
Fuzzy Sets | p. 22 |
Rough Sets | p. 23 |
Emergence of Rough-Fuzzy Computing | p. 26 |
Granular Computing | p. 26 |
Computational Theory of Perception and f-Granulation | p. 26 |
Rough-Fuzzy Computing | p. 28 |
Generalized Rough Sets | p. 29 |
Entropy Measures | p. 30 |
Conclusion and Discussion | p. 36 |
References | p. 37 |
Rough-Fuzzy Clustering: Generalized c-Means Algorithm | p. 47 |
Introduction | p. 47 |
Existing c-Means Algorithms | p. 49 |
Hard c-Means | p. 49 |
Fuzzy c-Means | p. 50 |
Possibilistic c-Means | p. 51 |
Rough c-Means | p. 52 |
Rough-Fuzzy-Possibilistic c-Means | p. 53 |
Objective Function | p. 54 |
Cluster Prototypes | p. 55 |
Fundamental Properties | p. 56 |
Convergence Condition | p. 57 |
Details of the Algorithm | p. 59 |
Selection of Parameters | p. 60 |
Generalization of Existing c-Means Algorithms | p. 61 |
RFCM: Rough-Fuzzy c-Means | p. 61 |
RPCM: Rough-Possibilistic c-Means | p. 62 |
RCM: Rough c-Means | p. 63 |
FPCM: Fuzzy-Possibilistic c-Means | p. 64 |
FCM: Fuzzy c-Means | p. 64 |
PCM: Possibilistic c-Means | p. 64 |
HCM: Hard c-Means | p. 65 |
Quantitative Indices for Rough-Fuzzy Clustering | p. 65 |
Average Accuracy, ¿ Index | p. 65 |
Average Roughness, ¿ Index | p. 67 |
Accuracy of Approximation, ¿* Index | p. 67 |
Quality of Approximation, ¿ Index | p. 68 |
Performance Analysis | p. 68 |
Quantitative Indices | p. 68 |
Synthetic Data Set: X32 | p. 69 |
Benchmark Data Sets | p. 70 |
Conclusion and Discussion | p. 80 |
References | p. 81 |
Rough-Fuzzy Granulation and Pattern Classification | p. 85 |
Introduction | p. 85 |
Pattern Classification Model | p. 87 |
Class-Dependent Fuzzy Granulation | p. 88 |
Rough-Set-Based Feature Selection | p. 90 |
Quantitative Measures | p. 95 |
Dispersion Measure | p. 95 |
Classification Accuracy, Precision, and Recall | p. 96 |
¿ Coefficient | p. 96 |
ß Index | p. 97 |
Description of Data Sets | p. 97 |
Completely Labeled Data Sets | p. 98 |
Partially Labeled Data Sets | p. 99 |
Experimental Results | p. 100 |
Statistical Significance Test | p. 102 |
Class Prediction Methods | p. 103 |
Performance on Completely Labeled Data | p. 103 |
Performance on Partially Labeled Data | p. 110 |
Conclusion and Discussion | p. 112 |
References | p. 114 |
Fuzzy-Rough Feature Selection using f-Information Measures | p. 117 |
Introduction | p. 117 |
Fuzzy-Rough Sets | p. 120 |
Information Measure on Fuzzy Approximation Spaces | p. 121 |
Fuzzy Equivalence Partition Matrix and Entropy | p. 121 |
Mutual Information | p. 123 |
f-Information and Fuzzy Approximation Spaces | p. 125 |
V-Information | p. 125 |
I_{¿}-Information | p. 126 |
M_{¿}-Information | p. 127 |
¿_{¿}-Information | p. 127 |
Hellinger Integral | p. 128 |
Renyi Distance | p. 128 |
f-Information for Feature Selection | p. 129 |
Feature Selection Using f-Information | p. 129 |
Computational Complexity | p. 130 |
Fuzzy Equivalence Classes | p. 131 |
Quantitative Measures | p. 133 |
Fuzzy-Rough-Set-Based Quantitative Indices | p. 133 |
Existing Feature Evaluation Indices | p. 133 |
Experimental Results | p. 135 |
Description of Data Sets | p. 136 |
Illustrative Example | p. 137 |
Effectiveness of the FEPM-Based Method | p. 138 |
Optimum Value of Weight Parameter ß | p. 141 |
Optimum Value of Multiplicative Parameter ¿ | p. 141 |
Performance of Different f-Information Measures | p. 145 |
Comparative Performance of Different Algorithms | p. 152 |
Conclusion and Discussion | p. 156 |
References | p. 156 |
Rough Fuzzy c-Medoids and Amino Acid Sequence Analysis | p. 161 |
Introduction | p. 161 |
Bio-Basis Function and String Selection Methods | p. 164 |
Bio-Basis Function | p. 164 |
Selection of Bio-Basis Strings Using Mutual Information | p. 166 |
Selection of Bio-Basis Strings Using Fisher Ratio | p. 167 |
Fuzzy-Possibilistic c-Medoids Algorithm | p. 168 |
Hard c-Medoids | p. 168 |
Fuzzy c-Medoids | p. 169 |
Possibilistic c-Medoids | p. 170 |
Fuzzy-Possibilistic c-Medoids | p. 171 |
Rough-Fuzzy c-Medoids Algorithm | p. 172 |
Rough c-Medoids | p. 172 |
Rough-Fuzzy c-Medoids | p. 174 |
Relational Clustering for Bio-Basis String Selection | p. 176 |
Quantitative Measures | p. 178 |
Using Homology Alignment Score | p. 178 |
Using Mutual Information | p. 179 |
Experimental Results | p. 181 |
Description of Data Sets | p. 181 |
Illustrative Example | p. 183 |
Performance Analysis | p. 184 |
Conclusion and Discussion | p. 196 |
References | p. 196 |
Clustering Functionally Similar Genes from Microarray Data | p. 201 |
Introduction | p. 201 |
Clustering Gene Expression Data | p. 203 |
it-Means Algorithm | p. 203 |
Self-Organizing Map | p. 203 |
Hierarchical Clustering | p. 204 |
Graph-Theoretical Approach | p. 204 |
Model-Based Clustering | p. 205 |
Density-Based Hierarchical Approach | p. 206 |
Fuzzy Clustering | p. 206 |
Rough-Fuzzy Clustering | p. 206 |
Quantitative and Qualitative Analysis | p. 207 |
Silhouette Index | p. 207 |
Eisen and Cluster Profile Plots | p. 207 |
Z Score | p. 208 |
Gene-Ontology-Based Analysis | p. 208 |
Description of Data Sets | p. 209 |
Fifteen Yeast Data | p. 209 |
Yeast Sporulation | p. 211 |
Auble Data | p. 211 |
Cho et al. Data | p. 211 |
Reduced Cell Cycle Data | p. 211 |
Experimental Results | p. 212 |
Performance Analysis of Rough-Fuzzy c-Means | p. 212 |
Comparative Analysis of Different c-Means | p. 212 |
Biological Significance Analysis | p. 215 |
Comparative Analysis of Different Algorithms | p. 215 |
Performance Analysis of Rough-Fuzzy-Possibilistic c-Means | p. 217 |
Conclusion and Discussion | p. 217 |
References | p. 220 |
Selection of Discriminative Genes from Microarray Data | p. 225 |
Introduction | p. 225 |
Evaluation Criteria for Gene Selection | p. 227 |
Statistical Tests | p. 228 |
Euclidean Distance | p. 228 |
Pearson's Correlation | p. 229 |
Mutual Information | p. 229 |
f-Information Measures | p. 230 |
Approximation of Density Function | p. 230 |
Discretization | p. 231 |
Parzen Window Density Estimator | p. 231 |
Fuzzy Equivalence Partition Matrix | p. 233 |
Gene Selection using Information Measures | p. 234 |
Experimental Results | p. 235 |
Support Vector Machine | p. 235 |
Gene Expression Data Sets | p. 236 |
Performance Analysis of the FEPM | p. 236 |
Comparative Performance Analysis | p. 250 |
Conclusion and Discussion | p. 250 |
References | p. 252 |
Segmentation of Brain Magnetic Resonance Images | p. 257 |
Introduction | p. 257 |
Pixel Classification of Brain MR Images | p. 259 |
Performance on Real Brain MR Images | p. 260 |
Performance on Simulated Brain MR Images | p. 263 |
Segmentation of Brain MR Images | p. 264 |
Feature Extraction | p. 265 |
Selection of Initial Prototypes | p. 274 |
Experimental Results | p. 277 |
Illustrative Example | p. 277 |
Importance of Homogeneity and Edge Value | p. 278 |
Importance of Discriminant Analysis-Based Initialization | p. 279 |
Comparative Performance Analysis | p. 280 |
Conclusion and Discussion | p. 283 |
References | p. 283 |
Index | p. 287 |
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