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Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics (Advanced Information and Knowledge Processing) - Softcover
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.
"synopsis" may belong to another edition of this title.
From the Back Cover:
Review:
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.
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)"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2008
- ISBN 10 1848820488
- ISBN 13 9781848820487
- BindingPerfect Paperback
- Edition number1
- Number of pages632
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