Ecological Computations Series (ECS):
Vol. 6
Multivariate Data Analysis
in Ecology and Systematics
A methodological guide to the SYN-TAX 5.0 package
János Podani
1994
SPB Academic Publishing bv
Contents
Preface 7
Chapter 1. Introduction 11
Chapter 2. Data types and standardization 13
2.1 Types of raw data 13
2.2 The data matrix and its geometric interpretation 17
2.3 Data standardization and transformation 19
Chapter 3. Expressing resemblance 31
3.1 Resemblance measures for binary data 32
3.2 Resemblance measures for quantitative data 38
3.3 Resemblance measures for mixed data 44
3.4 Extensions to more than two objects (heterogeneity measures) 46
Chapter 4. Non-hierarchical clustering 51
4.1 K-means clustering 52
4.2 Global optimization 58
4.3 Multiple partitioning 62
4.4 Quick clustering 64
4.5 Fuzzy clustering 69
Chapter 5. Hierarchical clustering 77
5.1 Agglomerative methods 78
5.2 Divisive methods 98
5.3 Minimum spanning trees 102
Chapter 6. Ordination and related methods 107
6.1 Principal components analysis (PCA) 108
6.2 Correspondence analysis 122
6.3 Metric multidimensional scaling 128
6.4 Non-metric multidimensional scaling (NMDS) 136
6.5 Canonical variates analysis (CVA) 143
6.6 Canonical correlation analysis (CCA) 153
6.7 Eigenanalysis of symmetric matrices 162
Chapter 7. Rearrangement of matrices 163
7.1 Block clustering 164
7.2 Seriation 173
Chapter 8. Evaluation of results 181
8.1 Comparisons 181
8.1.1 Intra-type comparisons 184
8.1.2 Inter-type comparisons 235
8.2 Importance of variables in clustering 242
8.3 Optimal number of clusters in a classification 248
Chapter 9. Character ranking 253
9.1 Ranking by dispersion criteria 255
9.2 Ranking by information theory criteria 256
Chapter 10. Simulated sampling and analysis of multispecies
point patterns 263
10.1 Simulated sampling 264
10.2 The scale of pattern: information theory measures 271
10.3 The scale of pattern: expected resemblance 285
Glossary 289
References 301
Subject index 313