Clustering in Bioinformatics and Drug Discovery

235 Pages·2010·5.811 MB·\235

by  John David MacCuish (Author), Norah E. MacCuish (Author)

Clustering in
Bioinformatics
and Drug
Discovery
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Clustering in
Bioinformatics
and Drug
Discovery
John D. MacCuish
Norah E. MacCuish
CRC Press
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Contents
List of Figures
List of Tables
Preface
Acknowledgments
About the Authors
List of Symbols
Foreword
1 Introduction 1
1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Bioinformatics and Drug Discovery . . . . . . . . . . . . . . 13
1.3 Statistical Learning Theory and Exploratory Data Analysis . 16
1.4 Clustering Algorithms . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Computational Complexity . . . . . . . . . . . . . . . . . . . 18
1.5.1 Data Structures. . . . . . . . . . . . . . . . . . . . . . 21
1.5.2 Parallel Algorithms. . . . . . . . . . . . . . . . . . . . 23
1.6 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Data 27
2.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Binary Data . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Count Data . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.3 Continuous Data . . . . . . . . . . . . . . . . . . . . . 32
2.1.4 Categorical Data . . . . . . . . . . . . . . . . . . . . . 32
2.1.5 Mixed Type Data . . . . . . . . . . . . . . . . . . . . 32
2.2 Normalization and Scaling . . . . . . . . . . . . . . . . . . . 33
2.3 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Data Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Measures of Similarity . . . . . . . . . . . . . . . . . . . . . . 37
2.6.1 Binary Data Measures . . . . . . . . . . . . . . . . . . 38
2.6.1.1 The Tanimoto or Jaccard Measure . . . . . . 39
2.6.1.2 The Baroni-Urbani/BuserCoefficient . . . . 41
2.6.1.3 The Simple Matching Coefficient . . . . . . . 42
2.6.1.4 The Binary Euclidean Measure . . . . . . . . 46
2.6.1.5 The Binary Cosine or Ochai Measure . . . . 46
2.6.1.6 The Hamann Measure . . . . . . . . . . . . . 47
2.6.1.7 Other Binary Measures . . . . . . . . . . . . 47
2.6.2 Count Data Measures . . . . . . . . . . . . . . . . . . 49
2.6.2.1 The Tanimoto Count Measure . . . . . . . . 49
2.6.2.2 The Cosine Count Measure . . . . . . . . . . 50
2.6.3 Continuous Data Measures . . . . . . . . . . . . . . . 50
2.6.3.1 Continuous andWeighted Forms of Euclidean
Distance . . . . . . . . . . . . . . . . . . . . 50
2.6.3.2 Manhattan Distance . . . . . . . . . . . . . . 51
2.6.3.3 L∞ or Supremum Norm . . . . . . . . . . . . 51
2.6.3.4 Cosine. . . . . . . . . . . . . . . . . . . . . . 51
2.6.3.5 PearsonCorrelationCoefficient . . . . . . . . 52
2.6.3.6 Mahalanobis Distance . . . . . . . . . . . . . 52
2.6.4 Mixed Type Data . . . . . . . . . . . . . . . . . . . . 53
2.7 Proximity Matrices . . . . . . . . . . . . . . . . . . . . . . . 53
2.8 Symmetric Matrices . . . . . . . . . . . . . . . . . . . . . . . 53
2.8.1 Asymmetric Matrices . . . . . . . . . . . . . . . . . . 55
2.8.2 Hadamard Product of Two Matrices . . . . . . . . . . 56
2.8.3 Ultrametricity . . . . . . . . . . . . . . . . . . . . . . 57
2.8.4 Positive Semidefinite Matrices. . . . . . . . . . . . . . 57
2.9 Dimensionality, Components, Discriminants . . . . . . . . . . 57
2.9.1 Principal Component Analysis (PCA) . . . . . . . . . 58
2.9.1.1 Covariance Matrix . . . . . . . . . . . . . . . 58
2.9.1.2 Singular Value Decomposition . . . . . . . . 59
2.9.2 Non-Negative Matrix Factorization . . . . . . . . . . . 59
2.9.3 Multidimensional Scaling . . . . . . . . . . . . . . . . 59
2.9.4 Discriminants . . . . . . . . . . . . . . . . . . . . . . . 60
2.9.4.1 Fisher’s Linear Discriminant . . . . . . . . . 60
2.10 Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.11 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3 Clustering Forms 69
3.1 Partitional . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 Hierarchical . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2.1 Dendrograms and Heatmaps . . . . . . . . . . . . . . 73
3.3 Mixture Models . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5 Overlapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.6 Fuzzy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.7 Self-Organizing . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.8 Hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.9 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 Partitional Algorithms 91
4.1 K-Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.1 K-Medoid . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.1.2 K-Modes . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.1.3 Online K-Means . . . . . . . . . . . . . . . . . . . . . 94
4.2 Jarvis-Patrick . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3 Spectral Clustering . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . . . 99
4.5 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Cluster Sampling Algorithms 103
5.1 Leader Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 Taylor-Butina Algorithm . . . . . . . . . . . . . . . . . . . . 107
5.3 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6 Hierarchical Algorithms 113
6.1 Agglomerative . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.1.1 Reciprocal Nearest Neighbors Class of Algorithms . . 114
6.1.1.1 Complete Link . . . . . . . . . . . . . . . . . 114
6.1.1.2 Group Average . . . . . . . . . . . . . . . . . 114
6.1.1.3 Wards . . . . . . . . . . . . . . . . . . . . . . 115
6.1.2 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2 Divisive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7 Hybrid Algorithms 121
7.1 Self-Organizing Tree Algorithm . . . . . . . . . . . . . . . . 121
7.2 Divisive HierarchicalK-Means . . . . . . . . . . . . . . . . . 123
7.3 Exclusion Region Hierarchies . . . . . . . . . . . . . . . . . . 124
7.4 Biclustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.5 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127