Mathematical classification and clustering:
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
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Nonconvex optimization and its applications
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | 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 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 |
| Physical Description: | XV, 428 S. graph. Darst. |
| ISBN: | 0792341597 9781461380573 |
Staff View
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| 490 | 1 | |a Nonconvex optimization and its applications |v 11 | |
| 520 | 3 | |a 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 | |
| 520 | |a 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 | ||
| 520 | |a 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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Record in the Search Index
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| adam_text | MATHEMATICAL CLASSIFICATION AND CLUSTERING BY BORIS MIRKIN DIMACS,
RUTGERS UNIVERSITY KM FI KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON /
LONDON TABLE OF CONTENTS FOREWORD IX PREFACE XI 1 CLASSES AND CLUSTERS 1
1.1 CLASSIFICATION: A REVIEW 2 CLASSIFICATION IN THE SCIENCES.
DISCUSSION 1.2 FORMS AND PURPOSES OF CLASSIFICATION 18 FORMS OF
CLASSIFICATION. PURPOSES OF THE CLASSIFICATION. CONTENT OF THE
CLASSIFICA- TION. WHAT IS CLUSTERING? DISCUSSION 1.3 TABLE DATA AND ITS
TYPES 25 KINDS OF DATA. COLUMN-CONDITIONAL DATA TABLE. COMPARABLE DATA
TABLES. AG- GREGATE DATA TABLES. DISCUSSION 1.4 COLUMN-CONDITIONAL DATA
AND CLUSTERING 33 BOOLEAN DATA TABLE: TASKS AND DIGITS. EXAMPLES OF
QUANTITATIVE ENTITY-TO- VARIABLE DATA: IRIS, DISORDERS AND BODY. MIXED
VARIABLE TABLES: PLANETS AND RUSSIAN MASTERPIECES. DISCUSSION 1.5
CLUSTERING PROBLEMS FOR COMPARABLE DATA 41 ENTITY-TO-ENTITY DISTANCE
DATA: PRIMATES. ENTITY-TO-ENTITY SIMILARITY DATA: FUNCTIONS. THREE-WAY
SIMILARITY MATRIX: KINSHIP. ENTITY-TO-ENTITY INTERACTION TABLE:
CONFUSION. VARIABLE-TO-VARIABLE CORRELATION TABLE: ACTIVITIES. CATEGORY-
TO-CATEGORY PROXIMITY TABLE: BEHAVIOR. GRAPHS AND BINARY RELATIONS.
DISCUSSION 1.6 CLUSTERING PROBLEMS FOR AGGREGABLE DATA 53
CATEGORY-TO-CATEGORY DATA: WORRIES. INTERACTION DATA: MOBILITY AND
SWITCHING. DISCUSSION 2 GEOMETRY OF DATA 59 2.1 COLUMN-CONDITIONAL DATA
60 THREE DATA/CLUSTERING APPROACHES. STANDARDIZATION OF QUANTITATIVE
ENTITY-TO- VARIABLE DATA. QUANTITATIVE REPRESENTATION FOR MIXED DATA.
DISCUSSION 1 X 2.2 TRANSFORMATION OF COMPARABLE DATA 78 PRELIMINARY
TRANSFORMATION OF THE SIMILARITY DATA. DISSIMILARITY AND DISTANCE DATA.
GEOMETRY OF AGGREGABLE DATA. BOOLEAN DATA AND GRAPHS. DISCUSSION 2.3
LOW-RANK APPROXIMATION OF DATA 91 SVD AND PRINCIPAL COMPONENT ANALYSIS.
ORDINATION OF THE SIMILARITY DATA. COR- RESPONDENCE ANALYSIS FACTORS.
GREEDY APPROXIMATION OF THE DATA: SEFIT. FILLING IN MISSING DATA.
DISCUSSION 3 CLUSTERING ALGORITHMS: A REVIEW 109 3.1 A TYPOLOGY OF
CLUSTERING ALGORITHMS HO BASIC CHARACTERISTICS. OUTPUT CLUSTER
STRUCTURE. CRITERIA. ALGORITHMIC ASPECTS OF OPTIMIZATION. INPUT/OUTPUT
CLASSES. DISCUSSION 3.2 A SURVEY OF CLUSTERING TECHNIQUES 128 SINGLE
CLUSTER SEPARATION. PARTITIONING. HIERARCHICAL CLUSTERING. BICLUSTERING.
CONCEPTUAL CLUSTERING. SEPARATING SURFACE AND NEURAL NETWORK CLUSTERING.
PROB- ABILISTIC CLUSTERING. DISCUSSION 3.3 INTERPRETATION AIDS 158
VISUAL DISPLAY. VALIDATION. INTERPRETATION AS ACHIEVING THE CLUSTERING
GOALS. DISCUSSION 4 SINGLE CLUSTER CLUSTERING 169 4.1 SUBSET AS A
CLUSTER STRUCTURE 170 PRESENTATION OF SUBSETS. COMPARISON OF THE
SUBSETS. DISCUSSION 4.2 SERIATION: HEURISTICS AND CRITERIA 178
ONE-BY-ONE SERIATION. SERIATION AS LOCAL SEARCH. CLUSTERNESS OF THE
OPTIMAL CLUS- TERS. SERIATION WITH RETURNS. A CLASS OF GLOBALLY
OPTIMIZED CRITERIA. DISCUSSION 4.3 MOVING CENTER 194 CONSTANT RADIUS
METHOD. REFERENCE POINT METHOD. DISCUSSION 4.4 APPROXIMATION:
COLUMN-CONDITIONAL DATA 198 PRINCIPAL CLUSTER. IDEAL TYPE FUZZY
CLUSTERING. DISCUSSION 4.5 APPROXIMATION: COMPARABLE/AGGREGABLE DATA 206
VII ADDITIVE CLUSTERS. STAR CLUSTERING. BOX CLUSTERING. APPROXIMATION
CLUSTERING FOR THE AGGREGABLE DATA. DISCUSSION 4.6 MULTI CLUSTER
APPROXIMATION 217 SPECIFYING SEFIT PROCEDURE. EXAMPLES. DISCUSSION. 5
PARTITION: SQUARE DATA TABLE 229 5.1 PARTITION STRUCTURES 230
REPRESENTATION. LOADED PARTITIONS. DIVERSITY. COMPARISON OF PARTITIONS.
DISCUS- SION 5.2 ADMISSIBILITY IN AGGLOMERATIVE CLUSTERING 246 SPACE AND
STRUCTURE CONSERVING PROPERTIES. MONOTONE ADMISSIBILITY. OPTIMALITY
CRITERION FOR FLEXIBLE LW-ALGORITHMS. DISCUSSION 5.3 UNIFORM
PARTITIONING 254 DATA-BASED VALIDITY CRITERIA. MODEL FOR
UNIFORM-THRESHOLD PARTITIONING. LOCAL SEARCH ALGORITHMS. INDEX-DRIVEN
CONSENSUS PARTITIONS. DISCUSSION 5.4 ADDITIVE CLUSTERING 263 THE MODEL.
AGGLOMERATIVE ALGORITHM. SEQUENTIAL FITTING ALGORITHM. DISCUSSION 5.5
STRUCTURED PARTITION AND BLOCK MODEL 268 UNIFORM STRUCTURED PARTITION.
BLOCK MODELING. INTERPRETING BLOCK MODELING AS ORGANIZATION DESIGN.
DISCUSSION 5.6 AGGREGATION OF MOBILITY TABLES 278 APPROXIMATION MODEL.
MODELING AGGREGATE MOBILITY. DISCUSSION 6 PARTITION: RECTANGULAR DATA
TABLE 285 6.1 BILINEAR CLUSTERING FOR MIXED DATA 286 BILINEAR CLUSTERING
MODEL. LEAST-SQUARES CRITERION: CONTRIBUTIONS. LEAST-SQUARES CLUSTERING:
EQUIVALENT CRITERIA. LEAST-MODULI DECOMPOSITION. DISCUSSION 6.2 K-MEANS
AND BILINEAR CLUSTERING 298 PRINCIPAL CLUSTERING AND K-MEANS EXTENDED.
HOW K-MEANS PARAMETERS SHOULD BE CHOSEN. DISCUSSION 6.3
CONTRIBUTION-BASED ANALYSIS OF PARTITIONS 308 VIII * VARIABLE WEIGHTS.
APPROXIMATE CONJUNCTIVE CONCEPTS. SELECTING THE VARIABLES. TRANSFORMING
THE VARIABLE SPACE. KNOWLEDGE DISCOVERY. DISCUSSION 6.4 PARTITIONING IN
AGGREGABLE TABLES 320 ROW/COLUMN PARTITIONING BIPARTITIONING DISCUSSION
7 HIERARCHY AS A CLUSTERING STRUCTURE 329 7.1 REPRESENTING HIERARCHY 330
ROOTED LABELED TREE. INDEXED TREE AND ULTRAMETRIC. HIERARCHY AND
ADDITIVE STRUCTURE. NEST INDICATOR FUNCTION. EDGE-WEIGHTED TREE AND TREE
METRIE. T- SPLITS. NEIGHBORS RELATION. CHARACTER ROOTED TREES. COMPARING
HIERARCHIES. DISCUSSION 7.2 MONOTONE EQUIVARIANT METHODS 348 MONOTONE
EQUIVARIANCE AND THRESHOLD GRAPHS. ISOTONE CLUSTER METHODS. CLASSES OF
ISOTONE METHODS. DISCUSSION 7.3 ULTRAMETRICS AND TREE METRICS 354
ULTRAMETRIC AND MINIMUM SPANNING TREES. TREE METRIE AND ITS ADJUSTMENT.
DIS- CUSSION 7.4 SPLIT DECOMPOSITION THEORY 363 SPLIT METRICS AND
CANONICAL DECOMPOSITION. MATHEMATICAL PROPERTIES. WEAK CLUS- TERS AND
WEAK HIERARCHY. DISCUSSION 7.5 PYRAMIDS AND ROBINSON MATRICES 375
PYRAMIDS. LEAST-SQUARES FITTING. DISCUSSION 7.6 A LINEAR THEORY FOR
BINARY HIERARCHIES 384 BINARY HIERARCHY DECOMPOSITION OF A DATA MATRIX.
CLUSTER VALUE STRATEGY FOR DIVISIVE CLUSTERING. APPROXIMATION OF SQUARE
TABLES. DISCUSSION BIBLIOGRAPHY 399 INDEX 423
|
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| id | DE-604.BV011319311 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:07:44Z |
| institution | BVB |
| isbn | 0792341597 9781461380573 |
| language | English |
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| physical | XV, 428 S. graph. Darst. |
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| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Mirkin, Boris G. Verfasser aut Mathematical classification and clustering by Boris Mirkin Dordrecht [u.a.] Kluwer 1996 XV, 428 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 11 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 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 Clusteranalyse gtt Discriminantanalyse gtt Discriminant analysis Cluster analysis Cluster-Analyse (DE-588)4070044-6 gnd rswk-swf Klassifikationstheorie (DE-588)4164034-2 gnd rswk-swf Cluster-Analyse (DE-588)4070044-6 s Klassifikationstheorie (DE-588)4164034-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4613-0457-9 Nonconvex optimization and its applications 11 (DE-604)BV010085908 11 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007604671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mirkin, Boris G. Mathematical classification and clustering Nonconvex optimization and its applications Clusteranalyse gtt Discriminantanalyse gtt Discriminant analysis Cluster analysis Cluster-Analyse (DE-588)4070044-6 gnd Klassifikationstheorie (DE-588)4164034-2 gnd |
| subject_GND | (DE-588)4070044-6 (DE-588)4164034-2 |
| title | Mathematical classification and clustering |
| title_auth | Mathematical classification and clustering |
| title_exact_search | Mathematical classification and clustering |
| title_full | Mathematical classification and clustering by Boris Mirkin |
| title_fullStr | Mathematical classification and clustering by Boris Mirkin |
| title_full_unstemmed | Mathematical classification and clustering by Boris Mirkin |
| title_short | Mathematical classification and clustering |
| title_sort | mathematical classification and clustering |
| topic | Clusteranalyse gtt Discriminantanalyse gtt Discriminant analysis Cluster analysis Cluster-Analyse (DE-588)4070044-6 gnd Klassifikationstheorie (DE-588)4164034-2 gnd |
| topic_facet | Clusteranalyse Discriminantanalyse Discriminant analysis Cluster analysis Cluster-Analyse Klassifikationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007604671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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