Mathematical Tools for Data Mining Set Theory, Partial Orders, Combi
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),
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Dan A. Simovici Chabane Djeraba •
Mathematical Tools for Data Mining Set Theory, Partial Orders, Combinatorics
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Dan A. Simovici, MS, MS, PhD University of Massachusetts, Boston USA
AI&KP ISSN 1610-3947 ISBN: 978-1-84800-200-5 DOI: 10.1007/978-1-84800-201-2
Chabane Djeraba, BSc, MSc, PhD University of Sciences and Technologies of Lille (USTL) France
e-ISBN: 978-1-84800-201-2
British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2008932365 c Springer-Verlag London Limited 2008 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 Springer Science+Business Media springer.com
Preface
This volume was born from the experience of the authors as researchers and educators, which suggests that many students of data mining are handicapped in their research by the lack of a formal, systematic education in its mathematics. The data mining literature contains many excellent titles that address the needs of users with a variety of interests ranging from decision making to pattern investigation in biological data. However, these books do not deal with the mathematical tools that are currently needed by data mining researchers and doctoral students. We felt it timely to produce a book that integrates the mathematics of data mining with its applications. We emphasize that this book is about mathematical tools for data mining and not about data mining itself; despite this, a substantial amount of applications of mathematical concepts in data mining are presented. The book is intended as a reference for the working data miner. In our opinion, three areas of mathematics are vital for data mining: set theory, including partially ordered sets and combinatorics; linear algebra, with its many applications in principal component analysis and neural networks; and probability theory, which plays a foundational role in statistics, machine learning and data mining. This volume is dedicated to
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