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Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics

✍ Scribed by Dan A. Simovici, Chabane Djeraba (auth.)

Publisher
Springer-Verlag London
Year
2014
Tongue
English
Leaves
834
Series
Advanced information and knowledge processing
Edition
2
Category
Library
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✦ Synopsis

Data mining essentially relies on several mathematical disciplines, many of which are presented in this second edition of this book. Topics include partially ordered sets, combinatorics, general topology, metric spaces, linear spaces, graph theory. To motivate the reader a significant number of applications of these mathematical tools are included ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc. The book is intended as a reference for researchers and graduate students. The current edition is a significant expansion of the first edition. We strived to make the book self-contained and only a general knowledge of mathematics is required. More than 700 exercises are included and they form an integral part of the material. Many exercises are in reality supplemental material and their solutions are included.

✦ Table of Contents

Front Matter....Pages i-xi
Sets, Relations, and Functions....Pages 1-66
Partially Ordered Sets....Pages 67-95
Combinatorics....Pages 97-148
Topologies and Measures....Pages 149-195
Linear Spaces....Pages 197-279
Norms and Inner Products....Pages 281-345
Spectral Properties of Matrices....Pages 347-397
Metric Spaces Topologies and Measures....Pages 399-433
Convex Sets and Convex Functions....Pages 435-456
Graphs and Matrices....Pages 457-538
Lattices and Boolean Algebras....Pages 539-581
Applications to Databases and Data Mining....Pages 583-646
Frequent Item Sets and Association Rules....Pages 647-668
Special Metrics....Pages 669-725
Dimensions of Metric Spaces....Pages 727-766
Clustering....Pages 767-817
Back Matter....Pages 819-831

✦ Subjects

Data Mining and Knowledge Discovery; Mathematics of Computing; Discrete Mathematics in Computer Science; Computational Mathematics and Numerical Analysis

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