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

摘要： 混合鉴别分析（hybrid discirminant analysis，HDA）融合了主元分析和线性鉴别分析的优点，适合更多的数据分布，在实际应用中取得了较好的效果。然而HDA不适合复杂、非线性数据结构的维数约简。首先通过特征映射把数据样本映射到高维线性空间，然后建立线性HDA模型，基于流形学习理论和LSSVM（least square support vector machine）框架，给出了保持数据局部结构的核HDA（locality preserving kernel HDA，LPKHDA）算法。提出了基于散度矩阵的诱导核空间选择方法，通过把模型参数选择问题转化为最优诱导核空间选择问题来求取最优模型参数，通过梯度下降法求取核函数参数和散度矩阵系数最优值。基于Adaboost实现了LPKHDA算法。在UCI数据和人脸图像上进行仿真实验，结果表明与HDA算法相比，新算法不仅较好地解决了模型参数选择问题，且具有较好的性能。

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