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.

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.