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Mathematical Tools for Data Mining

Set Theory, Partial Orders, Combinatorics

  • Book
  • © 2014

Overview

Authors:
  1. Dan A. Simovici

    1. University of Massachusetts, Boston Dept. Computer Science, Boston, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Chabane Djeraba

    1. University Lille 1, Laboratoire d'Informatique Fundamentale de Lille, Villeneuve d'Ascq, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Focuses on mathematical topics of immediate interest to data mining and machine learning
  • The mathematics is illustrated by significant applications ranging from association rules, clustering algorithms, classification, data constraints, logical data analysis, etc
  • Includes more than 700 exercises and solutions
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Sets, Relations, and Functions

    • Dan A. Simovici, Chabane Djeraba
    Pages 1-66

  3. Partially Ordered Sets

    • Dan A. Simovici, Chabane Djeraba
    Pages 67-95

  4. Combinatorics

    • Dan A. Simovici, Chabane Djeraba
    Pages 97-148

  5. Topologies and Measures

    • Dan A. Simovici, Chabane Djeraba
    Pages 149-195

  6. Linear Spaces

    • Dan A. Simovici, Chabane Djeraba
    Pages 197-279

  7. Norms and Inner Products

    • Dan A. Simovici, Chabane Djeraba
    Pages 281-345

  8. Spectral Properties of Matrices

    • Dan A. Simovici, Chabane Djeraba
    Pages 347-397

  9. Metric Spaces Topologies and Measures

    • Dan A. Simovici, Chabane Djeraba
    Pages 399-433

  10. Convex Sets and Convex Functions

    • Dan A. Simovici, Chabane Djeraba
    Pages 435-456

  11. Graphs and Matrices

    • Dan A. Simovici, Chabane Djeraba
    Pages 457-538

  12. Lattices and Boolean Algebras

    • Dan A. Simovici, Chabane Djeraba
    Pages 539-581

  13. Applications to Databases and Data Mining

    • Dan A. Simovici, Chabane Djeraba
    Pages 583-646

  14. Frequent Item Sets and Association Rules

    • Dan A. Simovici, Chabane Djeraba
    Pages 647-668

  15. Special Metrics

    • Dan A. Simovici, Chabane Djeraba
    Pages 669-725

  16. Dimensions of Metric Spaces

    • Dan A. Simovici, Chabane Djeraba
    Pages 727-766

  17. Clustering

    • Dan A. Simovici, Chabane Djeraba
    Pages 767-817

  18. Back Matter

    Pages 819-831
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About this book

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.

Reviews

From the book reviews:

“This textbook is appropriate for an advanced undergraduate or graduate mathematics elective class. All theorems are proved, notation is standard, and ample exercise sets are included at the end of every chapter. … Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics is more than just the data-mining reference book. It is highly readable textbook that successfully connects classic, theoretical mathematics to an enormously popular current application in modern society.” (Susan D’Agostino, MAA Reviews, March, 2015)

“The goal of this book is to present the basic mathematical theory and principles used in data mining tools and techniques. … Graduate or advanced undergraduate students with prior coursework in mathematics will find this book a useful collection of the fundamental mathematical ideas … . The exposition of concepts is clear and readable. Comfort with mathematical notation is necessary, since the book makes significant use of such notation. Several exercises are included, with solutions being provided in outline.” (R. M. Malyankar, Computing Reviews, September, 2014)

Authors and Affiliations

  • University of Massachusetts, Boston Dept. Computer Science, Boston, USA

    Dan A. Simovici

  • University Lille 1, Laboratoire d'Informatique Fundamentale de Lille, Villeneuve d'Ascq, France

    Chabane Djeraba

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