Support Vector Machines
This book explains the principles that make support vector machines (SVMs) a successful modelling and prediction tool for a variety of applications. The authors present the basic ideas of SVMs together with the latest developments and current research que
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Information Science and Statistics
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Ingo Steinwart
•
Andreas Christmann
Support Vector Machines
ABC
Ingo Steinwart Information Sciences Group (CCS-3) Los Alamos National Laboratory Los Alamos, NM 87545 USA Series Editors
Michael Jordan Division of Computer Science and Department of Statistics University of California, Berkeley Berkeley, CA 94720 USA
Andreas Christmann University of Bayreuth Department of Mathematics Chair of Stochastics 95440 Bayreuth Germany Jon Kleinberg Department of Computer Science Cornell University Ithaca, NY 14853 USA
Bernhard Sch¨olkopf Max Planck Institute for Biological Cybernetics Spemmannstrasse 38 72076 T¨ubingen Germany R is a trademark of California Statistical Software, Inc. and is licensed exclusively to Salford Systems. CART° R is a trademark of Salford Systems. TreeNet°
IBM Intelligent Miner is a trademark of the International Business Machines Corporation. R and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute SAS° Inc. in the USA and other countries. R is a registered trademark of SPSS Inc. SPSS°
JavaTM is a trademark or registered trademark of Sun Microsystems, Inc. in the United States and other countries. Oracle is a registered trademark of Oracle Corporation and/or its affiliates. IMSL is a registered trademark of Visual Numerics, Inc. Previously published material included in the book: Portions of Section 4.4 are based on: I. Steinwart, D. Hush, and C. Scovel (2006), An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels. IEEE Trans. Inf. Theory, 52, 4635–4643 c °2006 IEEE. Reprinted, with permission. Portions of Section 9.4 are based on: A. Christmann and I. Steinwart (2008), Consistency of kernel based quantile regression. Appl. Stoch. Models Bus. Ind., 24, 171–183. c °2008 John Wiley & Sons, Ltd. Reproduced with permission.
ISBN: 978-0-387-77241-7 e-ISBN: 978-0-387-77242-4 DOI: 10.1007/978-0-387-77242-4 Library of Congress Control Number: 2008932159 c 2008 Springer Science+Business Media, LLC ° All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper 987654321 springer.com
F¨ ur Wiebke, Johanna, Wenke und Anke. (I.S.) F¨ ur Anne, Hanna, Thomas und meine Eltern. (A.C.)
Preface
Every mathematical
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