Cluster Analysis: A Survey

1. The Cluster Problem and Preliminary Ideas.- 1.1 Basic Notions and Definitions.- 1.2 The Cluster Problem.- 1.3 Distance Functions.- 1.4 Measures of Similarity.- 1.5 Distance and Similarity Between Clusters.- 1.6 Cluster Methods Based on Euclidean Distance.- 1.7 An Algorithm for Hierarchical Clustering.- 1.8 Other Aspects of the Cluster Problem.- 2. Clustering by Complete Enumeration.- 2.1 Introduction.- 2.2 The Number of Partitions of n Objects into m Non-empty Subsets.- 2.3 Recursive Relation for Stirling's Numbers of the Second Kind.- 2.4 Computational Aspects of Complete Enumeration.- 3. Mathematical Programming and Cluster Analysis.- 3.1 Application of Dynamic Programming to the Cluster Problem.- 3.2 Jensen's Dynamic Programming Model.- 3.3 Integer Programming Applications to Cluster Analysis.- 4. Similarity Matrix Representations.- 4.1 Dendograms.- 4.2 Comparison of Dendograms or Their Similarity Matrices.- 4.3 Basic Definitions.- 4.4 Trees.- 4.5 Local Operations on Trees.- 5. Clustering Based on Density Estimation.- 5.1 Mode Analysis.- 5.2 Probability Density Function Estimation.- 5.3 Clustering Based on Density Estimation.- 5.4 Remarks.- 6. Applications.- 6.1 Application to Remote Sensing Data.- 6.2 Application of Density Estimation Technique to Fisher's Iris Data.- 7. Historical Comments.- References.