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E-raamat: Clustering Methodology for Symbolic Data

(Universite de Paris IX - Dauphine, France), (University of Georgia, Athens)
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Covers everything readers need to know about clustering methodology for symbolic dataincluding new methods and headingswhile providing a focus on multi-valued list data, interval data and histogram data

This book presents all of the latest developments in the field of clustering methodology for symbolic datapaying special attention to the classification methodology for multi-valued list, interval-valued and histogram-valued data methodology, along with numerous worked examples. The book also offers an expansive discussion of data management techniques showing how to manage the large complex dataset into more manageable datasets ready for analyses.

Filled with examples, tables, figures, and case studies, Clustering Methodology for Symbolic Data begins by offering chapters on data management, distance measures, general clustering techniques, partitioning, divisive clustering, and agglomerative and pyramid clustering. 





Provides new classification methodologies for histogram valued data reaching across many fields in data science Demonstrates how to manage a large complex dataset into manageable datasets ready for analysis Features very large contemporary datasets such as multi-valued list data, interval-valued data, and histogram-valued data Considers classification models by dynamical clustering Features a supporting website hosting relevant data sets 

Clustering Methodology for Symbolic Data will appeal to practitioners of symbolic data analysis, such as statisticians and economists within the public sectors. It will also be of interest to postgraduate students of, and researchers within, web mining, text mining and bioengineering.
1 Introduction
1(6)
2 Symbolic Data: Basics
7(40)
2.1 Individuals, Classes, Observations, and Descriptions
8(1)
2.2 Types of Symbolic Data
9(8)
2.2.1 Multi-valued or Lists of Categorical Data
9(1)
2.2.2 Modal Multi-valued Data
10(2)
2.2.3 Interval Data
12(1)
2.2.4 Histogram Data
13(1)
2.2.5 Other Types of Symbolic Data
14(3)
2.3 How do Symbolic Data Arise?
17(7)
2.4 Descriptive Statistics
24(14)
2.4.1 Sample Means
25(1)
2.4.2 Sample Variances
26(2)
2.4.3 Sample Covariance and Correlation
28(3)
2.4.4 Histograms
31(7)
2.5 Other Issues
38(9)
Exercises
39(2)
Appendix
41(6)
3 Dissimilarity, Similarity, and Distance Measures
47(36)
3.1 Some General Basic Definitions
47(8)
3.2 Distance Measures: List or Multi-valued Data
55(7)
3.2.1 Join and Meet Operators for Multi-valued List Data
55(1)
3.2.2 A Simple Multi-valued Distance
56(2)
3.2.3 Gowda-Diday Dissimilarity
58(2)
3.2.4 Ichino-Yaguchi Distance
60(2)
3.3 Distance Measures: Interval Data
62(17)
3.3.1 Join and Meet Operators for Interval Data
62(1)
3.3.2 Hausdorff Distance
63(5)
3.3.3 Gowda-Diday Dissimilarity
68(5)
3.3.4 Ichino-Yaguchi Distance
73(3)
3.3.5 De Carvalho Extensisons of Ichino-Yaguchi Distances
76(3)
3.4 Other Measures
79(4)
Exercises
79(3)
Appendix
82(1)
4 Dissimilarity, Similarity, and Distance Measures: Modal Data
83(36)
4.1 Dissimilarity/Distance Measures: Modal Multi-valued List Data
83(10)
4.1.1 Union and Intersection Operators for Modal Multi-valued List Data
84(1)
4.1.2 A Simple Modal Multi-valued List Distance
85(2)
4.1.3 Extended Multi-valued List Gowda-Diday Dissimilarity
87(3)
4.1.4 Extended Multi-valued List Ichino-Yaguchi Dissimilarity
90(3)
4.2 Dissimilarity/Distance Measures: Histogram Data
93(26)
4.2.1 Transformation of Histograms
94(4)
4.2.2 Union and Intersection Operators for Histograms
98(3)
4.2.3 Descriptive Statistics for Unions and Intersections
101(3)
4.2.4 Extended Gowda-Diday Dissimilarity
104(4)
4.2.5 Extended Ichino-Yaguchi Distance
108(4)
4.2.6 Extended de Carvalho Distances
112(3)
4.2.7 Cumulative Density Function Dissimilarities
115(2)
4.2.8 Mallows' Distance
117(1)
Exercises
118(1)
5 General Clustering Techniques
119(30)
5.1 Brief Overview of Clustering
119(1)
5.2 Partitioning
120(5)
5.3 Hierarchies
125(6)
5.4 Illustration
131(15)
5.5 Other Issues
146(3)
6 Partitioning Techniques
149(48)
6.1 Basic Partitioning Concepts
150(3)
6.2 Multi-valued List Observations
153(6)
6.3 Interval-valued Data
159(10)
6.4 Histogram Observations
169(8)
6.5 Mixed-valued Observations
177(2)
6.6 Mixture Distribution Methods
179(7)
6.7 Cluster Representation
186(3)
6.8 Other Issues
189(8)
Exercises
191(2)
Appendix
193(4)
7 Divisive Hierarchical Clustering
197(64)
7.1 Some Basics
197(6)
7.1.1 Partitioning Criteria
197(3)
7.1.2 Association Measures
200(3)
7.2 Monothetic Methods
203(33)
7.2.1 Modal Multi-valued Observations
205(9)
7.2.2 Non-modal Multi-valued Observations
214(2)
7.2.3 Interval-valued Observations
216(9)
7.2.4 Histogram-valued Observations
225(11)
7.3 Polythethic Methods
236(14)
7.4 Stopping Rule R
250(7)
7.5 Other Issues
257(4)
Exercises
258(3)
8 Agglomerative Hierarchical Clustering
261(56)
8.1 Agglomerative Hierarchical Clustering
261(28)
8.1.1 Some Basic Definitions
261(5)
8.1.2 Multi-valued List Observations
266(3)
8.1.3 Interval-valued Observations
269(9)
8.1.4 Histogram-valued Observations
278(3)
8.1.5 Mixed-valued Observations
281(1)
8.1.6 Interval Observations with Rules
282(7)
8.2 Pyramidal Clustering
289(28)
8.2.1 Generality Degree
289(8)
8.2.2 Pyramid Construction Based on Generality Degree
297(12)
8.2.3 Pyramids from Dissimilarity Matrix
309(3)
8.2.4 Other Issues
312(1)
Exercises
313(2)
Appendix
315(2)
References 317(14)
Index 331
LYNNE BILLARD, PHD, is University Professor in the Department of Statistics at the University of Georgia, USA. She has over two hundred and twenty-five publications mostly in leading journals, and co-edited six books. Professor Billard is a former president of ASA, IBS, and ENAR.

EDWIN DIDAY, PHD, is the Professor of Computer Science at Centre De Recherche en Mathematiques de la Decision, CEREMADE, Université Paris-Dauphine, Université PSL, Paris, France. He has published fifty-eight papers and authored or edited fourteen books. Professor Diday is also the founder of the Symbolic Data Analysis field.