Mathematical Classification and Clustering

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Springer Science & Business Media, Aug 31, 1996 - Mathematics - 448 pages
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I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in this book is quite interesting and stimulating in paradigms, clustering and optimization. On the other hand, it has a substantial application appeal. The book will be useful both to specialists and students in the fields of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. Panos Pardalos, Series Editor.
 

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Contents

Classes and Clusters
1
a Review
2
12 Forms and Purposes of Classification
18
13 Table Data and Its Types
25
14 ColumnConditional Data and Clustering
33
15 Clustering Problems for Comparable Data
41
16 Clustering Problems for Aggregable Data
53
Geometry of Data Sets
59
Partition Square Data Table
229
51 Partition Structures
230
52 Admissibility in Agglomerative Clustering
246
53 Uniform Partitioning
254
54 Additive Clustering
263
55 Structured Partition and Block Model
268
56 Aggregation of Mobility Tables
278
Partition Rectangular Data Table
285

21 ColumnConditional Data
60
22 Transformation of Comparable Data
78
23 LowRank Approximation of Data
91
Clustering Algorithms a Review
109
31 A Typology of Clustering Algorithms
110
32 A Survey of Clustering Techniques
128
33 Interpretation Aids
158
Single Cluster Clustering
169
41 Subset as a Cluster Structure
170
Heuristics and Criteria
178
43 Moving Center
194
ColumnConditional Data
198
ComparableAggregable Data
206
46 Multi Cluster Approximation
217
61 Bilinear Clustering for Mixed Data
286
62 KMeans and Bilinear Clustering
298
63 ContributionBased Analysis of Partitions
308
64 Partitioning in Aggregable Tables
320
Hierarchy as a Clustering Structure
329
71 Representing Hierarchy
330
72 Monotone Equivariant Methods
348
73 Ultrametrics and Tree Metrics
354
74 Split Decomposition Theory
363
75 Pyramids and Robinson Matrices
375
76 A Linear Theory for Binary Hierarchies
384
Bibliography
399
Index
423
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Page 400 - H.-J. Bandelt and A. Dress. Reconstructing the shape of a tree from observed dissimilarity data.
Page 411 - Arabie, P. (1994). The analysis of proximity matrices through sums of matrices having (anti-)Robinson forms.
Page 410 - In: IJ Cox, P. Hansen, and B. Julesz (Eds.) Partitioning Data Sets. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, 105-116.
Page 401 - Baulieu, FB (1989) A classification of presence/absence based dissimilarity coefficients. Journal of Classification, 6, 233-46.
Page 405 - WS (1982). GENNCLUS: New models for general nonhierarchical clustering analysis. Psychometrika, 47, 446-449.

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