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A Study on Kernel-based Classification and Dimension Reduction and Its Application

Author: LiuZhongBao
Tutor: WangShiTong
School: Jiangnan University
Course: Light Industry Information Technology and Engineering
Keywords: Linear Discriminant Analysis (LDA) Beam angle Fuzzy techniques Kerneldensity estimation Entropy theory Privacy-preserving Large scale datasets
CLC: TP391.4
Type: PhD thesis
Year: 2012
Downloads: 325
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Abstract


Pattern classification and feature reduction are two of important tasks in pattern recognition and their related techniques attract more and more attentions of the researchers. With the development of kernel methods, the range of traditional pattern recognition techniques is widely broadened. Many research results are used in data mining, image processing, speech recognition, fingerprint classification and medical diagnosis. However, current feature reduction and pattern classification methods show drawbacks of low robustness and weak generalization ability to a certain extent. In order to solve the above problems, several issues are addressed in this dissertation:Firstly, several improved Linear Discriminant Analysis (LDA) are proposed to deal with the rank limitation problem and small sample size problem in traditional LDA: Modified Linear Discriminant Analysis based on Linear Combination of K-order Matrices (MLDA) redefines within-class scatter matrix in order to make the traditional Fisher criterion get much more robust and adapt to practical applications. Scalarized Linear Discriminant Analysis (SLDA) introduces between-class scatter scalar and within-class scatter scalar and extracts features through computing the weight of each dimension in the sample space. Matrix Exponential Linear Discriminant Analysis (MELDA) also redefines the between-class scatter matrix and the within-class scatter matrix which can effectively extract the discriminative information included in the null subspace and non-null subspace of within-class scatter matrix. Besides, we provide an iterative convergence analysis of Fisher and Kernel Analysis algorithm (FKA) proposed by the paper “bilinear analysis for kernel selection and nonlinear feature extraction” using the concept of Radermacher complexity.Secondly, researches on current feature extraction methods are mainly based on two ways. One originates from geometric properties of high-dimensional datasets and attempt to extract fewer features from the original data space according to a certain criterion. The other originates from dimension reduction deviation and try to make the deviation between data before and after dimension reduction be as small as possible. However, there exists almost no any study about them from the perspective of the scatter change of a dataset. Based on Parzen window density estimator, we thoroughly revisit the relevant feature extraction methods from a new perspective and the relationships between Parzen window and LPP, LDA and PCA are built.Thirdly, hyperplane, hypersphere including ellipsoid are used in current boundary classification. Whether a spacial point can be used in classification is worthy to study. Inspired by space geometry and beam angle, a novel Maximum Margin Learning Machine based on Beam Angle (BAMLM) is proposed. In the view of optical, BAMLM is to find a light source to respectively irradiate two classes. In the view of space geometry, BAMLM is to find a classified point in the pattern space to separate two classes. Meanwhile, the kernel BAMLM is equivalent to the kernel Center-Constrained Minimum Enclosing Ball (CCMEB) and BAMLM can be extended to BACVM by introducing Core Vector Machine (CVM) which can work for large scale datasets. While the classification efficiency of BAMLM and BACVM are greatly influenced by the noise and isolated points, Maximum-margin Fuzzy Classifier based on Spacial Point (MFC) is proposed in which fuzzy techniques are introduced and the influences of the noise and isolated points are decreased.Forthly, in order to solve the problems of private preserving and large scale data classification in kernel SVM, Privacy-Preserving Learning Machine for Large Scale Datasets (PPLM) and Nonlinearly Assembling Learning Machine based on Separating Hyperplane (NALM) are proposed. In PPLM, CVM is firstly introduced to sample the large scale datasets, and then two points from different classes are chosen in the core set and the hyperplane orthogonal to the line connecting these two points is treated as the optimal separating hyperplane. PPLM can work for large scale datasets and performs well. In NALM, the original datasets are firstly divided into several subsets. After running the SH algorithm on each subset, we can obtain the final classification results through assembling each result from each subset. NALM is not only privacy-preserving, but also extends the usage of SH from small scale datasets to medium and large scale datasets and from linear space to Hilbert kernel space.In the last, the maximum-margin classification algorithms including SVM and its improved algorithms are widely used in practice, but these algorithms are greatly influenced by the affine or telescopic data. The main reason is that these algorithms only take the margin between classes into consideration while neglect the data distribution in each class. Therefore, Maximum-margin Learning Machine based on Entropy Theory and Kernel Density Estimation (MEKLM) is proposed to solve the drawback of the maximum-margin classification algorithms In MEKLM, data distributions in samples are represented by kernel density estimation and classification uncertainties are represented by entropy. MEKLM takes boundary data between classes and inner data in each class seriously, so it performs well. Meanwhile, it can work for two-class and one-class pattern classification.

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices
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