Full Description
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.
Contents
Preface.- Acknowledgements.- General Introduction. Methods and History.- Seriation from Proximity Variance Analysis.- Main Approachs in Seriation. The Attraction Pole Case.- Comparing Geometrical and Ordinal Seriation Methods in Formal and Real Cases.- A New Family of Combinatorial Algorithms in Seriation.- Clustering Methods from Proximity Variance Analysis.- Conclusion and Developments.
