Contents
0. Introduction 1
1. Sampling, data types 7
1.1 Sampling: basic terms 8
1.2 Sampling alternatives 9
1.3 Main characteristics of sampling 11
1.4 Data: measurement scales and other properties 20
1.5 Advanced topics 26
1.6 Literature overview 29
1.7 Imaginary dialogue 31
2. The data matrix and data transformation 33
2.1 The principle of attribute duality and the geometric meaning of data matrices 34
2.2 Displaying multivariate data structures by simple means 35
2.3 Data transformation and standardization 37
2.4 Literature overview 50
2.5 Imaginary dialogue 52
3. Distance, similarity, correlation... 55
3.1 Basic terms 55
3.2 Coefficients for binary data 59
3.3 Coefficients for nominal data 70
3.4 The case of ordinal variables 73
3.5 Coefficients for interval and ratio scale variables 76
3.6 Coefficients for mixed data 97
3.7 Generalization of distances to more than two objects (heterogeneity measures) 99
3.8 Literature overview 101
3.9 Imaginary dialogue 104
4. Non-hierarchical classification 111
4.1 Partitioning methods 113
4.2 Overlapping clusters 123
4.3 Fuzzy clustering 124
4.4 Literature overview 129
4.5 Imaginary dialogue 130
5. Hierarchical clustering 135
5.1 Algorithmic types 138
5.2 Agglomerative methods 139
5.3 Divisive algorithms 155
5.4 Special clustering procedures 158
5.5 Evaluation of hierarchical classifications 163
5.6 Literature overview 169
5.7 Imaginary dialogue 171
6. Cladistics 175
6.1 Basic principles and terms 176
6.2 Distance-based cladistics 180
6.3 Character-based reconstruction of evolutionary trees 186
6.4 Other possibilities for evaluating nucleotide sequences <196> in brief 202
6.5 Cladistic biogeography 205
6.6 Literature overview 208
6.7 Imaginary dialogue 210
7. Ordination 215
7.1 A fundamental ordination method: principal components analysis 216
7.2 Two groups of variables: canonical correlation analysis 234
7.3 Correspondence analysis 241
7.4 Multidimensional scaling 252
7.5 Separating gropups by ordination: canonical variates analysis 263
7.6 Morphometric ordination 270
7.7 Literature overview 278
7.8 Imaginary dialogue 281
8. Matrix rearrangement 285
8.1 The unequal importance of variables: character ranking 285
8.2 Block clustering 294
8.3 Seriation 302
8.4 Literature overview 307
8.5 Imaginary dialogue 308
9. Comparative evaluation of results 313
9.1 Main choices 314
9.2 Pairwise comparison of results 317
9.3 Hypothesis testing, expectations and distributions 331
9.4 The consensus approach 340
9.5 Comparison of results of the different type 348
9.6 Literature overview 350
9.7 Imaginary dialogue 351
Appendix A: Example data matrices 355
Appendix B: Availability of computer programs 361
Appendix C: A summary of matrix algebra 365
References 377
Subject index 401