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© 2014

Mathematical Tools for Data Mining

Set Theory, Partial Orders, Combinatorics

Benefits

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Dan A. Simovici, Chabane Djeraba
    Pages 1-66
  3. Dan A. Simovici, Chabane Djeraba
    Pages 67-95
  4. Dan A. Simovici, Chabane Djeraba
    Pages 97-148
  5. Dan A. Simovici, Chabane Djeraba
    Pages 149-195
  6. Dan A. Simovici, Chabane Djeraba
    Pages 197-279
  7. Dan A. Simovici, Chabane Djeraba
    Pages 281-345
  8. Dan A. Simovici, Chabane Djeraba
    Pages 347-397
  9. Dan A. Simovici, Chabane Djeraba
    Pages 399-433
  10. Dan A. Simovici, Chabane Djeraba
    Pages 435-456
  11. Dan A. Simovici, Chabane Djeraba
    Pages 457-538
  12. Dan A. Simovici, Chabane Djeraba
    Pages 539-581
  13. Dan A. Simovici, Chabane Djeraba
    Pages 583-646
  14. Dan A. Simovici, Chabane Djeraba
    Pages 647-668
  15. Dan A. Simovici, Chabane Djeraba
    Pages 669-725
  16. Dan A. Simovici, Chabane Djeraba
    Pages 727-766
  17. Dan A. Simovici, Chabane Djeraba
    Pages 767-817
  18. Back Matter
    Pages 819-831

About this book

Introduction

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.

Authors and affiliations

  1. 1.University of Massachusetts, Boston Dept. Computer ScienceBostonUSA
  2. 2.University Lille 1Laboratoire d'Informatique Fundamentale de LilleVilleneuve d'AscqFrance

Bibliographic information

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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)