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

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Overview

"The maturing of the field of data mining has brought about an increased level of mathematical sophistication. Such disciplines like topology, combinatorics, partially ordered sets and their associated algebraic structures (lattices and Boolean algebras), and metric spaces are increasingly applied in data mining research. This book presents these mathematical foundations of data mining integrated with applications to provide the reader with a comprehensive reference." Mathematics is presented in a thorough and rigorous manner offering a detailed
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Overview

"The maturing of the field of data mining has brought about an increased level of mathematical sophistication. Such disciplines like topology, combinatorics, partially ordered sets and their associated algebraic structures (lattices and Boolean algebras), and metric spaces are increasingly applied in data mining research. This book presents these mathematical foundations of data mining integrated with applications to provide the reader with a comprehensive reference." Mathematics is presented in a thorough and rigorous manner offering a detailed explanation of each topic, with applications to data mining such as frequent item sets, clustering, decision trees also being discussed. More than 400 exercises are included and they form an integral part of the material. Some of the exercises are in reality supplemental material and their solutions are included. The reader is assumed to have a knowledge of elementary analysis.
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"The book is organized into four parts, with a total of 15 chapters. Each chapter … offers numerous exercises and references for further reading. … Overall, Simovici and Djeraba’s presentation of both the theoretical grounds and the practical aspects of the various data mining methodologies is good. … The book is intended for readers who have a data mining background … . It will help this audience to improve their knowledge of how different data mining strategies operate from a mathematical standpoint." (Aris Gkoulalas-Divanis, ACM Computing Reviews, February, 2009)

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Product Details

Table of Contents

Pt. I Set Theory

1 Sets, Relations, and Functions 3

2 Algebras 57

3 Graphs and Hypergraphs 79

Pt. II Partial Orders

4 Partially Ordered Sets 129

5 Lattices and Boolean Algebras 173

6 Topologies and Measures 225

7 Frequent Item Sets and Association Rules 273

8 Applications to Databases and Data Mining 295

9 Rough Sets 333

Pt. III Metric Spaces

10 Dissimilarities, Metrics, and Ultrametrics 351

11 Topologies and Measures on Metric Spaces 423

12 Dimensions of Metric Spaces 459

13 Clustering 495

Pt. IV Combinatorics

14 Combinatorics 529

15 The Vapnik-Chervoucukis Dimension 551

Pt. V Appendices

Appendix A Asymptotics 571

Appendix B Convex Sets and Functions 573

Appendix C Useful Integrals and Formulas 583

Appendix D A Characterization of a Function 593

References 597

Topic Index 605

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