Principal Component Analysis [data, math. anal.]

300 Pages·2012·12.54 MB·English

by  P. Sanguansat

PRINCIPAL
COMPONENT ANALYSIS

Edited by Parinya Sanguansat
Principal Component Analysis
Edited by Parinya Sanguansat

Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia

Copyright © 2012 InTech
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Publishing Process Manager Oliver Kurelic
Technical Editor Teodora Smiljanic
Cover Designer InTech Design Team

First published March, 2012
Printed in Croatia

A free online edition of this book is available at www.intechopen.com
Additional hard copies can be obtained from [email protected]

Principal Component Analysis, Edited by Parinya Sanguansat
p. cm.
ISBN 978-953-51-0195-6

Contents

Preface IX
Chapter 1 Two-Dimensional Principal Component
Analysis and Its Extensions 1
Parinya Sanguansat
Chapter 2 Application of Principal Component Analysis to
Elucidate Experimental and Theoretical Information 23
Cuauhtémoc Araujo-Andrade, Claudio Frausto-Reyes,
Esteban Gerbino, Pablo Mobili, Elizabeth Tymczyszyn,
Edgar L. Esparza-Ibarra, Rumen Ivanov-Tsonchev
and Andrea Gómez-Zavaglia
Chapter 3 Principal Component Analysis:
A Powerful Interpretative Tool at the
Service of Analytical Methodology 49
Maria Monfreda
Chapter 4 Subset Basis Approximation of Kernel
Principal Component Analysis 67
Yoshikazu Washizawa
Chapter 5 Multilinear Supervised Neighborhood Preserving
Embedding Analysis of Local Descriptor Tensor 91
Xian-Hua Han and Yen-Wei Chen
Chapter 6 Application of Linear and Nonlinear
Dimensionality Reduction Methods 107
Ramana Vinjamuri, Wei Wang, Mingui Sun
and Zhi-Hong Mao
Chapter 7 Acceleration of Convergence of the
Alternating Least Squares Algorithm for
Nonlinear Principal Components Analysis 129
Masahiro Kuroda, Yuichi Mori, Masaya Iizuka
and Michio Sakakihara
VI Contents

Chapter 8 The Maximum Non-Linear
Feature Selection of Kernel
Based on Object Appearance 145
Mauridhi Hery Purnomo, Diah P. Wulandari,
I. Ketut Eddy Purnama and Arif Muntasa
Chapter 9 FPGA Implementation for
GHA-Based Texture Classification 165
Shiow-Jyu Lin, Kun-Hung Lin and Wen-Jyi Hwang
Chapter 10 The Basics of Linear
Principal Components Analysis 181
Yaya Keho
Chapter 11 Robust Density Comparison Using
Eigenvalue Decomposition 207
Omar Arif and Patricio A. Vela
Chapter 12 Robust Principal Component Analysis
for Background Subtraction: Systematic
Evaluation and Comparative Analysis 223
Charles Guyon, Thierry Bouwmans and El-hadi Zahzah
Chapter 13 On-Line Monitoring of Batch
Process with Multiway PCA/ICA 239
Xiang Gao
Chapter 14 Computing and Updating Principal Components
of Discrete and Continuous Point Sets 263
Darko Dimitrov

Preface

It is more than a century since Karl Pearson invented the concept of Principal
Component Analysis (PCA). Nowadays, it is a very useful tool in data analysis in
many fields. PCA is the technique of dimensionality reduction, which transforms
data in the high-dimensional space to space of lower dimensions. The advantages of
this subspace are numerous. First of all, the reduced dimension has the effect of
retaining the most of the useful information while reducing noise and other
undesirable artifacts. Secondly, the time and memory that used in data processing
are smaller. Thirdly, it provides a way to understand and visualize the structure of
complex data sets. Furthermore, it helps us identify new meaningful underlying
variables.
Indeed, PCA itself does not reduce the dimension of the data set. It only rotates the
axes of data space along lines of maximum variance. The axis of the greatest
variance is called the first principal component. Another axis, which is orthogonal to
the previous one and positioned to represent the next greatest variance, is called the
second principal component, and so on. The dimension reduction is done by using
only the first few principal components as a basis set for the new space. Therefore,
this subspace tends to be small and may be dropped with minimal loss of
information.
Originally, PCA is the orthogonal transformation which can deal with linear data.
However, the real-world data is usually nonlinear and some of it, especially
multimedia data, is multilinear. Recently, PCA is not limited to only linear
transformation. There are many extension methods to make possible nonlinear and
multilinear transformations via manifolds based, kernel-based and tensor-based
techniques. This generalization makes PCA more useful for a wider range of
applications.
In this book the reader will find the applications of PCA in many fields such as
image processing, biometric, face recognition and speech processing. It also includes
the core concepts and the state-of-the-art methods in data analysis and feature
extraction.
X Preface

Finally, I would like to thank all recruited authors for their scholarly contributions and
also to InTech staff for publishing this book, and especially to Mr.Oliver Kurelic, for
his kind assistance throughout the editing process. Without them this book could not
be possible. On behalf of all the authors, we hope that readers will benefit in many
ways from reading this book.

Parinya Sanguansat
Faculty of Engineering and Technology, Panyapiwat Institute of Management
Thailand