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Classification and Regression Trees.pdf
Dedication
Title Page
Copyright Page
PREFACE
Acknowledgements
Chapter 1 - BACKGROUND
1.1 CLASSIFIERS AS PARTITIONS
1.2 USE OF DATA IN CONSTRUCTING CLASSIFIERS
1.3 THE PURPOSES OF CLASSIFICATION ANALYSIS
1.4 ESTIMATING ACCURACY
1.5 THE BAYES RULE AND CURRENT CLASSIFICATION PROCEDURES
Chapter 2 - INTRODUCTION TO TREE CLASSIFICATION
2.1 THE SHIP CLASSIFICATION PROBLEM
2.2 TREE STRUCTURED CLASSIFIERS
2.3 CONSTRUCTION OF THE TREE CLASSIFIER
2.4 INITIAL TREE GROWING METHODOLOGY
2.5 METHODOLOGICAL DEVELOPMENT
2.6 TWO RUNNING EXAMPLES
2.7 THE ADVANTAGES OF THE TREE STRUCTURED APPROACH
Chapter 3 - RIGHT SIZED TREES AND HONEST ESTIMATES
3.1 INTRODUCTION
3.2 GETTING READY TO PRUNE
3.3 MINIMAL COST-COMPLEXITY PRUNING
3.4 THE BEST PRUNED SUBTREE: AN ESTIMATION PROBLEM
3.5 SOME EXAMPLES
APPENDIX
Chapter 4 - SPLITTING RULES
4.1 REDUCING MISCLASSIFICATION COST
4.2 THE TWO-CLASS PROBLEM
4.3 THE MULTICLASS PROBLEM: UNIT COSTS
4.4 PRIORS AND VARIABLE MISCLASSIFICATION COSTS
4.5 TWO EXAMPLES
4.6 CLASS PROBABILITY TREES VIA GINI
APPENDIX
Chapter 5 - STRENGTHENING AND INTERPRETING
5.1 INTRODUCTION
5.2 VARIABLE COMBINATIONS
5.3 SURROGATE SPLITS AND THEIR USES
5.4 ESTIMATING WITHIN-NODE COST
5.5 INTERPRETATION AND EXPLORATION
5.6 COMPUTATIONAL EFFICIENCY
5.7 COMPARISON OF ACCURACY WITH OTHER METHODS
APPENDIX
Chapter 6 - MEDICAL DIAGNOSIS AND PROGNOSIS
6.1 PROGNOSIS AFTER HEART ATTACK
6.2 DIAGNOSING HEART ATTACKS
6.3 IMMUNOSUPPRESSION AND THE DIAGNOSIS OF CANCER
6.4 GAIT ANALYSIS AND THE DETECTION OF OUTLIERS
6.5 RELATED WORK ON COMPUTER-AIDED DIAGNOSIS
Chapter 7 - MASS SPECTRA CLASSIFICATION
7.1 INTRODUCTION
7.2 GENERALIZED TREE CONSTRUCTION
7.3 THE BROMINE TREE: A NONSTANDARD EXAMPLE
Chapter 8 - REGRESSION TREES
8.1 INTRODUCTION
8.2 AN EXAMPLE
8.3 LEAST SQUARES REGRESSION
8.4 TREE STRUCTURED REGRESSION
8.5 PRUNING AND ESTIMATING
8.6 A SIMULATED EXAMPLE
8.7 TWO CROSS-VALIDATION ISSUES
8.8 STANDARD STRUCTURE TREES
8.9 USING SURROGATE SPLITS
8.10 INTERPRETATION
8.11 LEAST ABSOLUTE DEVIATION REGRESSION
8.12 OVERALL CONCLUSIONS
Chapter 9 - BAYES RULES AND PARTITIONS
9.1 BAYES RULE
9.2 BAYES RULE FOR A PARTITION
9.3 RISK REDUCTION SPLITTING RULE
9.4 CATEGORICAL SPLITS
Chapter 10 - OPTIMAL PRUNING
10.1 TREE TERMINOLOGY
10.2 OPTIMALLY PRUNED SUBTREES
10.3 AN EXPLICIT OPTIMAL PRUNING ALGORITHM
Chapter 11 - CONSTRUCTION OF TREES FROM A LEARNING SAMPLE
11.1 ESTIMATED BAYES RULE FOR A PARTITION
11.2 EMPIRICAL RISK REDUCTION SPLITTING RULE
11.3 OPTIMAL PRUNING
11.4 TEST SAMPLES
11.5 CROSS-VALIDATION
11.6 FINAL TREE SELECTION
11.7 BOOTSTRAP ESTIMATE OF OVERALL RISK
11.8 END-CUT PREFERENCE
Chapter 12 - CONSISTENCY
12.1 EMPIRICAL DISTRIBUTIONS
12.2 REGRESSION
12.3 CLASSIFICATION
12.4 PROOFS FOR SECTION 12.1
12.5 PROOFS FOR SECTION 12.2
12.6 PROOFS FOR SECTION 12.3
BIBLIOGRAPHY
NOTATION INDEX
SUBJECT INDEX
Table of Contents
Dedication
Title Page
Copyright Page
PREFACE
Acknowledgements
Chapter 1 - BACKGROUND
PROBLEM
3.5 SOME EXAMPLES
APPENDIX
2
1.1 CLASSIFIERS AS PARTITIONS
1.2 USE OF DATA IN CONSTRUCTING CLASSIFIERS
1.3 THE PURPOSES OF CLASSIFICATION ANALYSIS
1.4 ESTIMATING ACCURACY
1.5 THE BAYES RULE AND CURRENT CLASSIFICATION
PROCEDURES
Chapter 2 - INTRODUCTION TO TREE CLASSIFICATION
2.1 THE SHIP CLASSIFICATION PROBLEM
2.2 TREE STRUCTURED CLASSIFIERS
2.3 CONSTRUCTION OF THE TREE CLASSIFIER
2.4 INITIAL TREE GROWING METHODOLOGY
2.5 METHODOLOGICAL DEVELOPMENT
2.6 TWO RUNNING EXAMPLES
2.7 THE ADVANTAGES OF THE TREE STRUCTURED
APPROACH
Chapter 3 - RIGHT SIZED TREES AND HONEST ESTIMATES
3.1 INTRODUCTION
3.2 GETTING READY TO PRUNE
3.3 MINIMAL COST-COMPLEXITY PRUNING
3.4 THE BEST PRUNED SUBTREE: AN ESTIMATION
4.1 REDUCING MISCLASSIFICATION COST
4.2 THE TWO-CLASS PROBLEM
4.3 THE MULTICLASS PROBLEM: UNIT COSTS
4.4 PRIORS AND VARIABLE MISCLASSIFICATION COSTS
4.5 TWO EXAMPLES
4.6 CLASS PROBABILITY TREES VIA GINI
APPENDIX
Chapter 5 - STRENGTHENING AND INTERPRETING
5.1 INTRODUCTION
5.2 VARIABLE COMBINATIONS
5.3 SURROGATE SPLITS AND THEIR USES
5.4 ESTIMATING WITHIN-NODE COST
5.5 INTERPRETATION AND EXPLORATION
5.6 COMPUTATIONAL EFFICIENCY
5.7 COMPARISON OF ACCURACY WITH OTHER METHODS
APPENDIX
Chapter 6 - MEDICAL DIAGNOSIS AND PROGNOSIS
6.1 PROGNOSIS AFTER HEART ATTACK
6.2 DIAGNOSING HEART ATTACKS
6.3 IMMUNOSUPPRESSION AND THE DIAGNOSIS OF
CANCER
6.4 GAIT ANALYSIS AND THE DETECTION OF OUTLIERS
6.5 RELATED WORK ON COMPUTER-AIDED DIAGNOSIS
Chapter 7 - MASS SPECTRA CLASSIFICATION
7.1 INTRODUCTION
7.2 GENERALIZED TREE CONSTRUCTION
7.3 THE BROMINE TREE: A NONSTANDARD EXAMPLE
Chapter 4 - SPLITTING RULES
Chapter 8 - REGRESSION TREES
8.1 INTRODUCTION
8.2 AN EXAMPLE
3
8.3 LEAST SQUARES REGRESSION
8.4 TREE STRUCTURED REGRESSION
8.5 PRUNING AND ESTIMATING
8.6 A SIMULATED EXAMPLE
8.7 TWO CROSS-VALIDATION ISSUES
8.8 STANDARD STRUCTURE TREES
8.9 USING SURROGATE SPLITS
8.10 INTERPRETATION
8.11 LEAST ABSOLUTE DEVIATION REGRESSION
8.12 OVERALL CONCLUSIONS
Chapter 9 - BAYES RULES AND PARTITIONS
9.1 BAYES RULE
9.2 BAYES RULE FOR A PARTITION
9.3 RISK REDUCTION SPLITTING RULE
9.4 CATEGORICAL SPLITS
Chapter 10 - OPTIMAL PRUNING
10.1 TREE TERMINOLOGY
10.2 OPTIMALLY PRUNED SUBTREES
10.3 AN EXPLICIT OPTIMAL PRUNING ALGORITHM
Chapter 11 - CONSTRUCTION OF TREES FROM A LEARNING
SAMPLE
11.1 ESTIMATED BAYES RULE FOR A PARTITION
11.2 EMPIRICAL RISK REDUCTION SPLITTING RULE
11.3 OPTIMAL PRUNING
11.4 TEST SAMPLES
11.5 CROSS-VALIDATION
11.6 FINAL TREE SELECTION
11.7 BOOTSTRAP ESTIMATE OF OVERALL RISK
11.8 END-CUT PREFERENCE
Chapter 12 - CONSISTENCY
12.1 EMPIRICAL DISTRIBUTIONS
12.2 REGRESSION
4
12.3 CLASSIFICATION
12.4 PROOFS FOR SECTION 12.1
12.5 PROOFS FOR SECTION 12.2
12.6 PROOFS FOR SECTION 12.3
BIBLIOGRAPHY
NOTATION INDEX
SUBJECT INDEX
5
Lovingly dedicated to our children
Jessica, Rebecca, Kymm;
Melanie;
Elyse, Adam, Rachel, Stephen;
Daniel and Kevin
6
7
Library of Congress Cataloging-in-Publication Data
Main entry under title:
Classification and regession trees.
(The Wadsworth statistics/probability series)
Bibliography: p.
Includes Index.
ISBN 0-412-04841-8
1. Discriminant analysis. 2. Regression analysis.
3. Trees (Graph theory) I. Breiman, Leo. II. Title:
Regression trees. II. Series.
QA278.65.C54 1984
519.5′36—dc20
83-19708
CIP
This book contains information obtained from authentic and highly regarded sources. Reprinted
material is quoted with permission, and sources are indicated. A wide variety of references are
listed. Reasonable efforts have been made to publish reliable data and information, but the author
and the publisher cannot assume responsibility for the validity of all materials or for the
consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopying, microfilming, and recording, or by any
information storage or retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion,
for creating new works, or for resale. Specific permission must be obtained in writing from CRC
Press LLC for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
First CRC Press reprint 1998
© 1984, 1993 by Chapman & Hall
No claim to original U.S. Government works
International Standard Book Number 0-412-04841-8
Library of Congress Card Number 83-19708
Printed in the United States of America 7 8 9 0
Printed on acid-free paper
8
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