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Discriminant analysis based feature extraction for pattern recognition.

机译：基于判别分析的特征提取用于模式识别。

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摘要

Fisher's linear discriminant analysis (FLDA) has been widely used in pattern recognition applications. However, this method cannot be applied for solving the pattern recognition problems if the within-class scatter matrix is singular, a condition that occurs when the number of the samples is small relative to the dimension of the samples. This problem is commonly known as the small sample size (SSS) problem and many of the FLDA variants proposed in the past to deal with this problem suffer from excessive computational load because of the high dimensionality of patterns or lose some useful discriminant information. This study is concerned with developing efficient techniques for discriminant analysis of patterns while at the same time overcoming the small sample size problem. With this objective in mind, the work of this research is divided into two parts.;Inspired by the results of this theorem that essentially establishes a class separability of linearly independent samples in a specific discriminant subspace, in part 2, a new systematic framework for the pattern recognition of linearly independent samples is developed. Within this framework, a discriminant model, in which the samples of the individual classes of the dataset lie on parallel hyperplanes and project to single distinct points of a discriminant subspace of the underlying input space, is shown to exist. Based on this model, a number of algorithms that are devoid of the SSS problem are developed to obtain this discriminant subspace for datasets with linearly independent samples.;For the discriminant analysis of datasets for which the samples are not linearly independent, some of the linear algorithms developed in this thesis are also kernelized.;Extensive experiments are conducted throughout this investigation in order to demonstrate the validity and effectiveness of the ideas developed in this study. It is shown through simulation results that the linear and nonlinear algorithms for discriminant analysis developed in this thesis provide superior performance in terms of the recognition accuracy and computational complexity.;In part 1, a technique by solving the problem of generalized singular value decomposition (GSVD) through eigen-decomposition is developed for linear discriminant analysis (LDA). The resulting algorithm referred to as modified GSVD-LDA (MGSVD-LDA) algorithm is thus devoid of the singularity problem of the scatter matrices of the traditional LDA methods. A theorem enunciating certain properties of the discriminant subspace derived by the proposed GSVD-based algorithms is established. It is shown that if the samples of a dataset are linearly independent, then the samples belonging to different classes are linearly separable in the derived discriminant subspace; and thus, the proposed MGSVD-LDA algorithm effectively captures the class structure of datasets with linearly independent samples.
机译：Fisher的线性判别分析（FLDA）已被广泛用于模式识别应用中。但是，如果类内散射矩阵是奇异的，则该方法不能用于解决模式识别问题，这是当样本数相对于样本的维数较小时发生的情况。这个问题通常被称为小样本量（SSS）问题，并且过去为解决该问题而提出的许多FLDA变体由于图案的高维而遭受了过多的计算负荷，或者丢失了一些有用的判别信息。这项研究关注于开发有效的技术来进行模式判别分析，同时克服小样本量问题。考虑到这一目标，本研究工作分为两部分。受该定理结果的启发，该定理实质上建立了特定判别子空间中线性独立样本的类可分性，在第2部分中，提出了一种新的系统框架开发了线性独立样本的模式识别。在该框架内，存在一个判别模型，在该模型中，数据集各个类别的样本位于平行超平面上，并投影到基础输入空间的判别子空间的单个不同点。在此模型的基础上，开发了许多没有SSS问题的算法来获得具有线性独立样本的数据集的判别子空间。;对于对样本不是线性独立的数据集进行判别分析，一些线性本文还开发了一些算法。；在整个研究过程中进行了广泛的实验，以证明本研究中提出的思想的有效性和有效性。通过仿真结果表明，本文开发的线性和非线性判别分析算法在识别精度和计算复杂度方面均具有优越的性能。；第一部分，解决广义奇异值分解（GSVD）的技术）通过本征分解被开发用于线性判别分析（LDA）。因此，称为改进的GSVD-LDA（MGSVD-LDA）算法的所得算法没有传统LDA方法的散射矩阵的奇异性问题。建立了一个定理，该定理阐明了所提出的基于GSVD的算法所导出的判别子空间的某些属性。结果表明，如果一个数据集的样本是线性独立的，那么属于不同类别的样本在导出的判别子空间中是线性可分离的。因此，提出的MGSVD-LDA算法有效地捕获了具有线性独立样本的数据集的类结构。

著录项

  • 作者

    Wu, Wei.;

  • 作者单位

    Concordia University (Canada).;

  • 授予单位 Concordia University (Canada).;
  • 学科 Engineering Computer.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 140 p.
  • 总页数 140
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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