||In recent years, as the kernel extension of linear discriminant analysis (LDA), kernel discriminant analysis (KDA) has become one of popular and powerful tools for dimensionality reduction and feature extraction in fields of machine learning and pattern recognition, with superior performance in many practical applications. In this thesis, I investigate three adverse problems that can impair the performance of KDA in many real-world applications, and these problems are referred as: the small sample size problem, the outlier classes problem, and the heteroscedastic problem. In order to overcome the adverse problems for KDA, in this thesis, I also trend to propose three different weighted KDA methods: kernel fractional-step discriminant analysis (KFDA), complete kernel fraction-step discriminant analysis (CKFDA), and heteroscedastic kernel weighted discriminant analysis (HKWDA). KFDA effectively overcomes the adverse effects of outlier classes via a weighted Fisher criterion; CKFDA not effectively solves the outlier classes problem via the weighted discriminant criteria but only solves the small sample size problem via calculating the discriminant information in two orthogonal subspaces; HKWDA not effectively solves both the outlier classes problem and the heteroscedastic problem via a weighted chernoff criterion, but also considers the small sample size problem via simply calculating the crucial discriminant information in the null subspace of the within-class scatter. Extensive comparative studies performed on many face databases reveal the effectiveness of three weighted KDA methods proposed in this thesis.