| Description |
xviii, 179 pages : illustrations ; 26 cm + 1 CD-ROM (4 3/4 in.) |
| Series |
Interdisciplinary mathematical sciences ; v. 10 |
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Interdisciplinary mathematical sciences ; v. 10
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| Contents |
Contents note continued: 5.3.2.Kernels for residuated mapping on [∩]+0 -- 5.4.Normalized dissimilarities -- 5.5.Clustering connection for normalized residuated mappings -- 6.Clustering based on posets -- 6.1.Galois connections -- 6.2.Formal concept analysis -- 6.3.Boolean dissimilarities -- 6.4.Relational clustering -- 7.A new poset model -- 7.1.An informal approach -- 7.2.A more formal approach -- 7.3.Algorithms in the poset model -- 7.4.The software -- 7.5.The Majority induced order -- 7.6.Confidence interval clustering -- 7.7.Thoughts for the future |
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Machine generated contents note: 1.Informal background -- 1.1.Types of relations -- 1.2.Nine integer example -- 1.3.Mammal milk example -- 2.Dissimilarities and clusters -- 2.1.Getting more formal -- 2.2.Dendrograms and ultrametrics -- 2.3.The Jardine-Sibson model -- 2.4.Worked examples -- 2.5.Characterization of the family of clusters -- 2.6.ML-sets and complete-linkage clustering -- 3.Ordinal data -- 3.1.Monotone equivariance -- 3.2.Actions of isotone mappings -- 3.3.Flat and 0-flat cluster methods -- 3.4.Clustering based on bridges -- 3.4.1.Bridges and generalized bridges -- 3.4.2.Bridge removal clustering -- 3.4.3.Software considerations -- 4.Continuity and ordinal continuity -- 4.1.Notions of Limits -- 4.2.Continuity -- 4.3.Order continuity -- 5.Classification of monotone equivariant cluster methods -- 5.1.Classification kernels -- 5.2.The clustering connection -- 5.3.Kernels of residuated mappings -- 5.3.1.Residuated and residual mappings -- |
| Summary |
Most modern textbooks on cluster analysis are written from the standpoint of computer science, which give the background, description and implementation of computer algorithms. This book proclaims several firsts --- the first to present a broad mathematical treatment of the subject, the first that illustrates dissimilarities taking values in a poset, and the first to notice the connection with formal concept analysis which is a powerful tool for investigating hidden structures in large data sets. -- |
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The subject is presented from a mathematical viewpoint with careful definitions. All clearly stated axioms are illustrated with concrete examples. New ideas are introduced informally first, and then in a careful, systematic manner. Much of the material has not previously appeared in the literature. It is to be hoped that the book holds promising directive to launch a new research area that is based on graph theory, as well as partially ordered sets. It also suggests the cluster algorithms that can be used for practical applications. The emphasis will be largely on ordinal data and ordinal cluster methods. --Book Jacket |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Cluster analysis.
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Graph theory.
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Partially ordered sets.
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| LC no. |
2010281895 |
| ISBN |
9789814287203 (hbk.) |
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9814287202 (hbk.) |
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