Nonlinear Dimensionality Reduction
Methods of dimensionality reduction provide a way to understand and visualize the structure of complex data sets. Traditional methods like principal component analysis and classical metric multidimensional scaling suffer from being based on linear models.
- PDF / 23,034,282 Bytes
- 316 Pages / 441 x 666 pts Page_size
- 63 Downloads / 195 Views
Information Science and Statistics Akaike and Kitagawa: The Practice of Time Series Analysis. Bishop: Pattern Recognition and Machine Learning. Cowell, Dawid, Lauritzen, and Spiegelhalter: Probabilistic Networks and Expert Systems. Doucet, de Freitas, and Gordon: Sequential Monte Carlo Methods in Practice. Fine: Feedforward Neural Network Methodology. Hawkins and Olwell: Cumulative Sum Charts and Charting for Quality Improvement. Jensen and Nielsen: Bayesian Networks and Decision Graphs, Second Edition. Lee and Verleysen: Nonlinear Dimensionality Reduction. Marchette: Computer Intrusion Detection and Network Monitoring: A Statistical Viewpoint. Rissanen: Information and Complexity in Statistical Modeling. Rubinstein and Kroese: The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte Carlo Simulation, and Machine Learning. Studen´y: Probabilistic Conditional Independence Structures. Vapnik: The Nature of Statistical Learning Theory, Second Edition. Wallace: Statistical and Inductive Inference by Minimum Massage Length.
John A. Lee
Michel Verleysen
Nonlinear Dimensionality Reduction
John Lee Molecular Imaging and Experimental Radiotherapy Université catholique de Louvain Avenue Hippocrate 54/69 B-1200 Bruxelles Belgium [email protected]
Series Editors: Michael Jordan Division of Computer Science and Department of Statistics University of California, Berkeley Berkeley, CA 94720 USA
Michel Verleysen Machine Learning Group – DICE Université catholique de Louvain Place du Levant 3 B-1348 Louvain-la-Neuve Belgium [email protected]
Jon Kleinberg Department of Computer Science Cornell University Ithaca, NY 14853 USA
Bernhard Schölkopf Max Planck Institute for Biological Cybernetics Spemannstrasse 38 72076 Tübingen Germany
Library of Congress Control Number: 2006939149
ISBN-13: 978-0-387-39350-6
e-ISBN-13: 978-0-387-39351-3
Printed on acid-free paper. © 2007 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. 9 8 7 6 5 4 3 2 1 springer.com
To our families
Preface
Methods of dimensionality reduction are innovative and important tools in the fields of data analysis, data mining, and machine learning. They provide a way to understand and visualize the structure of complex data sets. Traditional methods like principal component analysis and classical metric multidimen
