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Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering de Israël César Lerman

Foundations and Methods in Combinatorial and Statistical Data Analysis and Clustering: Advanced Information and Knowledge Processing

Autor Israël César Lerman
en Limba Engleză Hardback – 4 apr 2016
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.
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Specificații

ISBN-13: 9781447167914
ISBN-10: 1447167910
Pagini: 672
Ilustrații: XXIV, 647 p. 54 illus.
Dimensiuni: 160 x 241 x 42 mm
Greutate: 1.11 kg
Ediția:1st edition 2016
Editura: Springer
Colecția Advanced Information and Knowledge Processing
Seria Advanced Information and Knowledge Processing

Locul publicării:London, United Kingdom

Public țintă

Research

Cuprins

Preface.- On Some Facets of the Partition Set of a Finite Set.- Two Methods of Non-hierarchical Clustering.- Structure and Mathematical Representation of Data.- Ordinal and Metrical Analysis of the Resemblance Notion.- Comparing Attributes by a Probabilistic and Statistical Association I.- Comparing Attributes by a Probabilistic and Statistical Association II.- Comparing Objects or Categories Described by Attributes.- The Notion of “Natural” Class, Tools for its Interpretation. The Classifiability Concept.- Quality Measures in Clustering.- Building a Classification Tree.- Applying the LLA Method to Real Data.- Conclusion and Thoughts for Future Works

Recenzii

“This book provides a synthetic and systematic presentation of clustering, combinatorial, and statistical data analysis. … the presentation is interesting and original. Keeping a smart balance between theoretical concepts and practical issues, the book is addressed to students and researchers interested in data mining, data analysis, and clustering.” (Florin Gorunescu, zbMATH 1338.62012, 2016)

Textul de pe ultima copertă

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.
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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.

Caracteristici

Offers a step-by-step process of the path of the data to the synthetic structure summarizing the data given by a hierarchical or non-hierarchical clustering Presents brand new principles and methods within the Data Mining field Examines ascendant agglomerative hierarchical clustering and Likelihood Linkage Analysis (LLA) clustering methods from metrical, algorithmic and computational aspects Includes supplementary material: sn.pub/extras

Notă biografică

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 desDonnées. 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.