Seriation in Combinatorial and Statistical Data Analysis

ISBN-13: 9783030926960 / Angielski / Miękka / 2023 / 277 str.

Isra?l C?sar Lerman; Henri Leredde

Opis

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.

Spis treści

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.

O autorze

The first position of Israël César Lerman was at the "Centre de Calcul" of the "Maison des Sciences de l'Homme" in 1966. The vocation of this laboratory was defined by the introduction of computer science in the human and social sciences. He prepared there his "doctorat ès sciences mathématiques".  The general subject of this is mathematical statistics and computer science. More specifically, the subject is classification and data analysis. The thesis was defended in January 1971  at the University of Paris 6, after being reported by Jean-Paul Benzécri. He was appointed professor at the Department of Mathematics and Computer Science of the University of Rennes 1, on October 1, 1973. He was, more specifically, assigned to the Department of Computer Science in 1985. He taught very different audiences data analysis, mathematics and statistics in relation to computer science. This, at all levels and especially at the highest level. Its research refers to the "Data and Knowledge Management"  of the IRISA  department. The status of emeritus allowed him to actively pursue its research. Its contribution concerns the combinatorial and statistical analysis of data in relation to Data Mining and Knowledge discovery. In his case, the mathematical structure of synthesis has a discrete character: partitions or orders on the set concerned. Two principles govern its approach. The first one is set theoretic and relational representation of the description and the second one is the principle of the likelihood of the link in the evaluation of similarities between observed structures (see Chaps. 3 to 11 in [3] and 5 and 6 in [4]). He has had important applications in different fields: Archeology, Digital imaging, Bioinformatics, Educational sciences, ... 

Published books: [1] Lerman, I.C. :  Les Bases de la Classification Automatique. Gauthier-Villars, 1970; [2] Lerman, I.C. :  Classification et Analyse Ordinale des Données. Dunod, 1981; [3] Lerman, I.C.:  Fundations and Methods in Combinatorial and Statistical Data Analysis and Clustering. SpringerNature 2016.

Teacher-researcher in Applied Mathematics and Computer Science, Henri Leredde worked as a member of the Mathematics department at Sorbonne Paris Nord University. He was Director of Studies for the "Telecom and Networks" part of the Sup Galilée engineering school. He is now an associate researcher at LAGA⁽¹⁾.  In addition, he is an archaeologist, specialist in Gallo-Roman pottery and also practices numerous aerial surveys in archeology as a pilot.

(1) - LAGA : Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539 and Department of Mathematics, Institut Galilée, Sorbonne Paris-Nord University.