Mathematical Classification and Clustering

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Springer Science & Business Media, Jan 1, 1996 - Computers - 428 pages
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The goal of the book is threefold; first, to serve as a reference for the enormous amount of existing clustering concepts and methods; second, to be used as a textbook; and, third, to present the author's and his Russian colleagues' results in the perspective of current developments. It contains several unique features: It is the only book to contain an up-to-date review of clustering including the most recent theories about discrete clustering structures (subsets, partitions, hierarchies etc.) in their relation to data. An approximation framework is developed as a major construct substantiating and extending such existing approaches as agglomerative clustering and K-means method, and leading to new methods such as box and ideal type clustering, uniform partitioning, aggregation of flow tables, and principal cluster analysis: The opening chapter is devoted to a review of classification and clustering goals and forms prior to defining the scope and goals of clustering. A dozen real-world illustrative examples are interwoven throughout the exposition. A/LISTA Audience: The book will be useful to both specialists and students in the field of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines.
  

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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
Copyright

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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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