关键词: 核混合鉴别分析, 核方法, 模型选择, 诱导核空间, 维数约简

Abstract: Hybrid discriminant analysis (HDA) which combines principal component analysis (PCA) with linear discriminant analysis (LDA) can achieve satisfying performance for data set following complex distribution. However, HDA can not work well for complex and nonlinear distributed data. Based on manifold learning and LSSVM (least square support vector machine), this paper proposes a kernel-induced space selection-based local preserving hybrid discriminant analysis (LPKHDA) algorithm to overcome these drawbacks. In this algorithm, the input data are firstly mapped into high dimensional feature space through nonlinear map and linear HDA is modeled in the feature space. This paper discusses a kernel-induced space selection approach based on divergence matrix, which transforms LPKHDA model selection to kernel-induced space selection for optimal model parameter, and uses gradient descent method to achieve kernel parameter and optimal divergence matrix coefficient. Based on Adaboost, LPKHDA algorithm (Boosted LPKHDA ) is implemented. Several applications and experiments on UCI and face data set show that the algorithm can effectively deal with the problems of the existing HDA algorithms and provide good performance.

Key words: kernel hybrid discriminant analysis, kernel method, model selection, kernel-induced space, dimensional reduction