Robust Two-Dimensional Linear Discriminant Analysis via Information Divergence
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Robust Two-Dimensional Linear Discriminant Analysis via Information Divergence Lei Zhang1,2
· Zhizheng Liang1,2
Accepted: 21 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Due to the complexities of collected data that may contain outliers and noises, many variants of LDA and 2DLDA have been proposed to address this problem and have shown that the improved methods produce much better performance than classical LDA and 2DLDA. In this paper we propose a novel two-dimensional linear discriminant analysis method via information divergence. The proposed method applies the weighted L21 norm to learn a robust projection matrix in the image space. In the proposed model, we introduce the weights into the within-class scatter and the total scatter simultaneously, and learn the weights by imposing information divergence on the objective functions. To handle the proposed model, we resort to Dinkelbach’s extended algorithm to solve the proposed ratio minimization problem. Considering the characteristics of the subproblems, we exploit an equivalent representation of subproblems which can be solved by alternating optimization techniques where each block of variables has good optimization properties. The proposed model not only overcomes the small-sample-size problem, but also suppresses outliers by an adaptively weighted scheme with the guidance of information divergences. The experiments on several image data sets demonstrate that the classification performance of the proposed method is superior to that of some existing methods in the presence of outliers. Keywords Discriminant analysis · Information divergence · L21 norm · Adaptive weighted scheme
1 Introduction Dimensionality reduction [1–4] is an effective tool in modern data analysis where data visualization and data classification are involved. Recent deep learning models [5–8] which
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Lei Zhang [email protected] Zhizheng Liang [email protected]
1
School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China
2
Digitization of Mine, Engineering Research Center of Ministry of Education, Xuzhou 221116, China
123
L. Zhang, Z. Liang
capture nonlinear features can be used to classify data directly. But deep learning models often require a large number of training samples to learn numerous parameters of models. In some cases obtaining sufficient training samples is infeasible, and classical data classification methods(dimensionality reduction plus classifiers) still play an important role in the case where the small-sample-size (SSS) problem appears. Principle component analysis (PCA) and linear discriminant analysis (LDA) are two of the widely used dimensionality reduction methods. PCA is an unsupervised learning mode and it finds the projection matrix by keeping as much information of data as possible. LDA aims at obtaining the projection matrix by maximizing the between-class distance and minimizing the within-class distance in the transformed space. Due to the simplicity
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