Handwritten Chinese character recognition (HCCR) is a typical pattern recognition problem with large category set and high dimensionality. A common and effective solution to overcome the high dimensionality is projecting the samples into a lower-dimensional subspace by linear discriminant analysis (LDA). However, LDA cannot always achieve a better subspace to separate all the classes because in HCCR, the categories are much larger than the number of dimensionality. Moreover, the large number of similar characters would cause serious overlap in the lower-dimensional subspace. In this thesis, we propose three improved algorithms to alleviate the limitation of LDA in multi-class classification and apply to the challenging problem of HCCR. For similar character recognition, we also present a critical region feature selection algorithm for improving the similar character discrimination capability. The main work and contributions are as follows: 1. We propose a Modified Linear Discriminant Analysis (MLDA) algorithm to alleviate the overlapping problem of traditional LDA. Based on the two-step view of LDA, we embedded the constraint of locality preservation, which avoid the overlap of the similar classes in the lower subspace. Experimental results on two handwritten Chinese Character recognition datasets demonstrated that our algorithm is superior to the traditional LDA algorithm. 2. We propose a worst case optimization algorithm called Maxi-min Discriminant Analysis (MMDA) to reduce the aliasing problem of traditional LDA in the lower-dimensional subspace for multi-class classification. In contrast to LDA that maximizes the separability in average sense, MMDA maximizes the divergence of nearest classes in the subspace so as to guarantee the worse-case seperability. We convert the new optimization criterion into a standard Semi-Definite Programming (SDP) problem based a reasonable relaxation, and proved that the relaxed formulation is equivalent to the primal problem under certain conditions. The experimental results on UCI datasets, Yale and ORL face datasets show that the proposed MMDA outperforms previous algorithms including LDA, aPAC, LFDA and LPP. 3. To overcome the complicated computation of the MMDA algorithm and make it applicable to problems of large-category set, we propose an online algorithm MMDAOnline algorithm. The MMDAOnline algorithm applies slack variables to MMDA criterion and replaces the SDP solution by online solution based on ...
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