Research On Robust Distance Measure Based Discriminant Analysis And Applications

Feature extraction plays an important role in pattern recognition and it aims at searching the mostefficient feature used for classification. Linear discriminant analysis (LDA) is one of therepresentatives and has already been successfully applied in many domains such as face recognition,text classification, information retrieval, etc. LDA aims at finding a optimal subspace of a set ofprojection directions that makes the between-class distance as maximal as possible while thewithin-class distance as minimal as possible in the reduced subspace. However, in the real world, dueto some inevitable reasons, there are usually a few noises or outliers mixed up with the data, therefore,it is significant to study the robust discriminant analysis (RDA). In recent years, although manyresearchers have developed some RDA algorithms, neither the inherent flaws of them nor theinterrelations among them have been deeply touched. Aiming at this problem, in this paper, we analyzeand compare the robustness among RDA algorithms based on different robust distance measures,further, leading to a classification of the existing RDA algorithms. Moreover, we propose some kinds ofgenerally RDA algorithms. The main researches and contributions are as follows:1. According to these robust methods, we classify the existing RDA algorithms, consequently, leadingto the directly-robustified DA (DRDA) and indirectly-robustified DA (IRDA).2. We propose a new kind of RDA algorithm, namely, robust discriminant analysis based onkernel-induced measure (KI-RDA). With the adopting of robust radial basis kernels (RBF), KI-RDAcan effectively deal with the data mixed with noise as well as the non-Gaussian distributed nonlineardata. It’s worthwhile to point that, due to the diversity of RBF functions, KI-RDA is actually a DPDAframework.3. We present a newly-devised indirectly-robustified DA framework, which utilizes a kind of robustprincipal component analysis (PCA), i.e., robust PCA based on kernel-induced measure (KI-PCA), toremove the outliers in data for clearing the holdback for following DA algorithms. Its robustness isaccredited to that KI-PCA makes use of the kernel-induced non-Euclidean (robust) distance instead ofthe Euclidean (nonrobust) distance in the objective. Experimental results on multifold datasets verifythe effectiveness of our method.4. From the theory and experiment, we analyze and compare the classification performance amongthe state-of-the-art RDA algorithms. Finally, according to the extensive experimental results, werepresent some significant conclusions, further, to prepare for our future researches.