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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.
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.
This monograph offers an original broad and very diverse
exploration of the seriation domain in data analysis, together with
building a specific relation to clustering.Relative to a data table
crossing a set of objects and a set of descriptive attributes, the
search for orders which correspond respectively to these two sets
is formalized mathematically and statistically. State-of-the-art
methods are created and compared with classical methods and a
thorough understanding of the mutual relationships between these
methods is clearly expressed. The authors distinguish two families
of methods: Geometric representation methods Algorithmic and
Combinatorial methods Original and accurate methods are provided in
the framework for both families. Their basis and comparison is made
on both theoretical and experimental levels. The experimental
analysis is very varied and very comprehensive. Seriation in
Combinatorial and Statistical Data Analysis has a unique character
in the literature falling within the fields of Data Analysis, Data
Mining and Knowledge Discovery. It will be a valuable resource for
students and researchers in the latter fields.
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