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© 2008

Mathematical Tools for Data Mining

Set Theory, Partial Orders, Combinatorics

Book

Part of the Advanced Information and Knowledge Processing book series (AI&KP)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Set Theory

    1. Front Matter
      Pages 1-1
    2. Dan A. Simovici, Chabane Djeraba
      Pages 3-55
    3. Dan A. Simovici, Chabane Djeraba
      Pages 57-77
    4. Dan A. Simovici, Chabane Djeraba
      Pages 79-125
  3. Partial Orders

    1. Front Matter
      Pages 127-127
    2. Dan A. Simovici, Chabane Djeraba
      Pages 129-172
    3. Dan A. Simovici, Chabane Djeraba
      Pages 173-224
    4. Dan A. Simovici, Chabane Djeraba
      Pages 225-272
    5. Dan A. Simovici, Chabane Djeraba
      Pages 273-293
    6. Dan A. Simovici, Chabane Djeraba
      Pages 295-332
    7. Dan A. Simovici, Chabane Djeraba
      Pages 333-348
  4. Metric Spaces

    1. Front Matter
      Pages 349-349
    2. Dan A. Simovici, Chabane Djeraba
      Pages 351-421
    3. Dan A. Simovici, Chabane Djeraba
      Pages 423-458
    4. Dan A. Simovici, Chabane Djeraba
      Pages 459-493
    5. Dan A. Simovici, Chabane Djeraba
      Pages 495-525
  5. Combinatorics

    1. Front Matter
      Pages 527-527
    2. Dan A. Simovici, Chabane Djeraba
      Pages 529-549
    3. Dan A. Simovici, Chabane Djeraba
      Pages 551-567

About this book

Introduction

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.

Features and topics:

• Study of functions and relations

• Applications are provided throughout

• Presents graphs and hypergraphs

• Covers partially ordered sets, lattices and Boolean algebras

• Finite partially ordered sets

• Focuses on metric spaces

• Includes combinatorics

• Discusses the theory of the Vapnik-Chervonenkis dimension of collections of sets

This wide-ranging, thoroughly detailed volume is self-contained and intended for researchers and graduate students, and will prove an invaluable reference tool.

Keywords

Boolean algebra Clustering combinatorics data mining database databases sets

Authors and affiliations

  1. 1.University of MassachusettsBostonUSA
  2. 2.University of Sciences and Technologies of Lille (USTL)France

Bibliographic information

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Reviews

From the reviews:

"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)