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Introduction to Pattern Recognition: A Matlab Approach
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An accompanying manual to Theodoridis/Koutroumbas, Pattern Recognition, that includes Matlab code of the most common methods and algorithms in the book, together with a descriptive summary and solved examples, and including real-life data sets in imaging and audio recognition.
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Academic Press is an imprint of Elsevier
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Copyright © 2010 Elsevier Inc. All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including
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Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with
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www.elsevier.com/permissions.
This book and the individual contributionscontained in it are protected under copyright by the Publisher
(other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing.As new research and experience broaden our understanding,
changes in research methods, professional practices, or medical treatment may become necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any
information, methods, compounds, or experiments described herein. In using such information or methods they should be
mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any
injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or
operation of any methods, products, instructions, or ideas contained in the material herein.
MATLAB
®
is a trademark of The MathWorks, Inc., and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB
®
software or related products does not
constitute endorsementor sponsorship by The MathWorks of a particular pedagogical approach or particular use of the
MATLAB
®
software.
Library of Congress Cataloging-in-Publication Data
Introduction to pattern recognition : a MATLAB
®
approach / Sergios Theodoridis … [et al.].
p. cm.
“Compliment of the book Pattern recognition, 4th edition, by S. Theodoridis and K. Koutroumbas,
Academic Press, 2009.”
Includes bibliographical references and index.
ISBN 978-0-12-374486-9 (alk. paper)
1. Pattern recognition systems. 2. Pattern recognition systems–Mathematics. 3. Numerical analysis.
4. MATLAB. I. Theodoridis, Sergios, 1951–. II. Theodoridis, Sergios, Pattern recognition.
TK7882.P3I65 2010
006.4–dc22
2010004354
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
For information on all Academic Press publications
visit our website at www.elsevierdirect.com
Printed in the United States
1011121314 10987654321
Preface
The aim of t hi s book is to serve pedagogi c goals as a complement of the book Pattern Recognition,
4th Edition, by S. Theodoridis and K. Kout roumbas (Academic Press, 2009). It is t he offspring of
our experience in teaching pattern recognition for a number of years to different audiences such as
students with good enough mathematical background, students who are more practice-oriented, pro-
fessional engineers, and computer scientists attending short t raining courses. The book unravel s along
two directions.
The first is to develop a set of MATLAB-based examples so that students wil l be able t o experiment
with methods and algorithms met in the various stages of designing a pattern recognition system—that
is, classifier design, feature select i on and generation, and syst em evaluat i on. To this end, we have made
an ef fort to “design” examples that will help the reader grasp the basics behind each method as well as
the respective cons and pros. In pattern recognition, there are no magic recipes that dictate which method
or technique to use for a speci fic problem. Very often, old good and simple (in concept) t echniques can
compete, from an efficiency point of vi ew, with more modern and elaborate techniques. To t his end,
that is, selecting the most appropriat e techni que, it is unfortunate that these days more and more people
follow the so-called black-box approach: try di fferent techniques, using a related S/W package t o play
with a set of paramet ers, even if the real meaning of these parameters is not really understood.
Such an “unsci entific” approach, which real l y prevents thought and creation, also deprives the
“user” of the ability to understand, explain, and interpret the obtained results. For this reason, most of
the examples in thi s book use simulated data. Hence, one can experiment with different paramet ers and
study the behavior of the respective method/algorithm. Havi ng control of the data, readers will be able
to “study,” “investigate,” and get familiar with the pros and cons of a technique. One can create data that
can push a technique to its “limits”—that is, where it fails. In addition, most of the real-life problems are
solved in high-dimensional spaces, where visualization is impossible; yet, visualizing geometry is one
of the most powerful and effective pedagogic tools so that a newcomer t o the field will be able t o “see”
how various methods work. The 3-dimensioanal space is one of t he most primitive and deep-rooted
experiences in the human brain because everyone is acquain ted with and has a good feeling about and
understanding of i t.
The second direction is to provide a summary of the relat ed theory, without mat hematics. We
have made an effort, as much as possible, to present the theory using arguments based on physical
reasoning, as well as point out the role of the various parameters and how they can influence t he
performance of a method/algorithm. Nevertheless, for a more thorough understanding, the mathematical
formulation cannot be bypassed. It is “there” where t he real worthy secrets of a method are, where the
deep understanding has its undisputable roots and grounds, where science li es. Theory and practice
are interrelated— one cannot be developed without the other. This is the reason that we consider this
book a complement of the prev iously published one. We consider it another branch leaning toward the
pract i cal side, the other branch being t he more theoretical one. Both branches are necessary to form the
pattern-recognitiontree, which has its roots i n the work of hundreds of researchers who have effortlessl y
contributed, over a number of decades, both in theory and practice.
ix
x Preface
All the MATLAB functions used throughout this book can be downloaded from the companion
website for this book at www.elsevierdirect .com/9780123744869. Note that, when running the MATLAB
code in the book, the results may slightly vary among different versions of MATLAB. Moreover, we
have made an effort to minimize dependencies on MATLAB toolboxes, as much as possible, and have
developed our own code.
Also, in spite of the careful proofreading of the book, it is still possible that some t ypos may
have escaped. The authors would appreciat e readers notifying them of any that are found, as well as
suggest i ons related t o the MATLAB code.
CHAPTER
1
Classifiers Based on Bayes
Decision Theory
1.1 INTRODUCTION
In this chapt er, we di scuss techniques inspired by Bayes decision theory. The theoretical developments
of the associated algorithms were given in [Theo 09, Chapter 2]. To the newcomer in the field of
pattern recognition the chapter’s algorithms and exercises are very important for developing a basic
understanding and familiarity with some fundamental notions associ ated with classification. Most of
the algorithms are simple in bot h structure and physical reasoning.
In a classification task, we are given a pattern and the task is to classify it into one out of c classes.
The number of classes, c, is assumed to be known a priori. Each pattern i s represented by a set of feature
values, x(i), i = 1,2, ...,l, which make up t he l-dimensi onal feature vector
1
x = [x(1),x(2), ..., x(l)]
T
∈
R
l
. We assume that each pattern is represented uniquely by a single feature vector and that it can belong
to only one class.
Given x ∈ R
l
and a set of c classes, ω
i
, i = 1, 2,..., c, the Bayes theory states t hat
P(ω
i
|x)p(x) = p(x |ω
i
)P(ω
i
) (1.1)
where
p(x) =
c
i=1
p(x|ω
i
)P(ω
i
)
where P(ω
i
) is the a priori probability of class ω
i
; i = 1, 2,..., c, P(ω
i
|x) is the a posteriori probability
of class ω
i
given the value of x; p(x) is the probability density function (pdf ) of x;andp(x|ω
i
), i =
1 = 2, ...,c, is the class conditional pdf of x given ω
i
(someti mes called t he likelihood of ω
i
with
respect to x).
1.2 BAYES DECISION THEORY
We are given a pattern whose class label i s unknown and we let x ≡ [x(1), x(2),...,x(l)]
T
∈ R
l
be
its corresponding feature vector, which results from some measurements. Also, we let the number of
possible classes be equal to c,thatis,ω
1
,..., ω
c
.
1
In contrast to [Theo 09], vector quantities are not boldfaced here in compliance with MATLAB notation.
Copyright © 2010 Elsevier Inc. All rights reserved.
DOI: 10.1016/B978-0-12-374486-9.00001-4
1
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