Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering

✍ Scribed by Israël César Lerman (auth.)

Publisher: Springer-Verlag London
Year: 2016
Tongue: English
Leaves: 664
Series: Advanced Information and Knowledge Processing
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book offers an original and broad exploration of the fundamental methods in Clustering and Combinatorial Data Analysis, presenting new formulations and ideas within this very active field.

With extensive introductions, formal and mathematical developments and real case studies, this book provides readers with a deeper understanding of the mutual relationships between these methods, which are clearly expressed with respect to three facets: logical, combinatorial and statistical.

Using relational mathematical representation, all types of data structures can be handled in precise and unified ways which the author highlights in three stages:

Clustering a set of descriptive attributes
Clustering a set of objects or a set of object categories
Establishing correspondence between these two dual clusterings

Tools for interpreting the reasons of a given cluster or clustering are also included.

Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering will be a valuable resource for students and researchers who are interested in the areas of Data Analysis, Clustering, Data Mining and Knowledge Discovery.

✦ Table of Contents

Front Matter....Pages i-xxiv
On Some Facets of the Partition Set of a Finite Set....Pages 1-59
Two Methods of Non-hierarchical Clustering....Pages 61-99
Structure and Mathematical Representation of Data....Pages 101-148
Ordinal and Metrical Analysis of the Resemblance Notion ....Pages 149-197
Comparing Attributes by Probabilistic and Statistical Association I....Pages 199-249
Comparing Attributes by a Probabilistic and Statistical Association II....Pages 251-323
Comparing Objects or Categories Described by Attributes....Pages 325-356
The Notion of “Natural” Class, Tools for Its Interpretation. The Classifiability Concept....Pages 357-433
Quality Measures in Clustering....Pages 435-512
Building a Classification Tree....Pages 513-582
Applying the LLA Method to Real Data....Pages 583-638
Conclusion and Thoughts for Future Works....Pages 639-647

✦ Subjects

Data Mining and Knowledge Discovery; Statistics and Computing/Statistics Programs; Combinatorics

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