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Mathematical Tools for Data Mining

Set Theory, Partial Orders, Combinatorics

By Dan A. Simovici , Chaabane Djeraba

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Offering the reader a reference to the mathematical tools required for data mining, this book integrates the mathematics of data mining with its applications. It provides the necessary mathematical background for researchers and graduate students.

Full Description

  • ISBN13: 978-1-8480-0200-5
  • 632 Pages
  • User Level: Science
  • Publication Date: August 15, 2008
  • Available eBook Formats: PDF
  • eBook Price: $149.00
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Full Description
This book integrates the mathematics of data mining with its applications, offering the reader a reference to the mathematical tools required for data mining. Dedicated to the study of set-theoretical foundations of data mining, this book is focused on set theory and several closely related areas: partially ordered sets and lattice theory, metric spaces and combinatorics. The book is structured into 4 parts and presents a comprehensive discussion of the subject. Features and topics include: - 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. Intended as a reference for the working data miner and researchers, a good knowledge of calculus is required to make the best use of this book, which will prove a useful reference.
Table of Contents

Table of Contents

  1. Set Theory.
  2. Sets, Relations, Functions.
  3. Algebras.
  4. Graphs and Hypergraphs.
  5. Partial Orders.
  6. Partially Ordered Sets.
  7. Lattices and Boolean Algebras.
  8. Topologies and Measures.
  9. Frequent Item Sets and Association Rules.
  10. Applications to Databases and Data Mining.
  11. Rough Sets.
  12. Metric Spaces.
  13. Dissimilarities, Metrics and Ultrametrics.
  14. Topologies and Measures on Metric Spaces.
  15. Dimensions of Metric Spaces.
  16. Clustering.
  17. Combinatorics.
  18. Combinatorics.
  19. Combinatorics and the Vapnik
  20. Chervonenkis Dimension.
  21. A: Asymptotics.
  22. B: Convex Sets and Functions.
  23. C: A Characterization of a Function.
  24. References.
  25. Topic Index.
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