Advanced Information and Knowledge Processing

Mathematical Tools for Data Mining

Set Theory, Partial Orders, Combinatorics

Authors: Simovici, Dan, Djeraba, Chabane

  • Integrates the mathematics of data mining with its applications
  • Comprehensive study of set-theoretical and combinatorial foundations of data mining
  • Provides the necessary mathematical background for researchers and graduate students
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  • ISBN 978-1-84800-201-2
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
About this book

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.

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)


Table of contents (15 chapters)

  • Sets, Relations, and Functions

    Simovici, Dan A. (et al.)

    Pages 3-55

  • Algebras

    Simovici, Dan A. (et al.)

    Pages 57-77

  • Graphs and Hypergraphs

    Simovici, Dan A. (et al.)

    Pages 79-125

  • Partially Ordered Sets

    Simovici, Dan A. (et al.)

    Pages 129-172

  • Lattices and Boolean Algebras

    Simovici, Dan A. (et al.)

    Pages 173-224

Buy this book

eBook n/a
  • ISBN 978-1-84800-201-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Tools for Data Mining
Book Subtitle
Set Theory, Partial Orders, Combinatorics
Authors
Series Title
Advanced Information and Knowledge Processing
Copyright
2008
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84800-201-2
DOI
10.1007/978-1-84800-201-2
Series ISSN
1610-3947
Edition Number
1
Number of Pages
XII, 615
Topics