核诱导距离度量的鲁棒判别分析

摘要

This paper proposes a robust discriminant analysis based on kernel-induced distance measure (KI-RDA). KI-RDA not only extends the linear discriminant analysis (LDA), but also extends the newest and powerful algorithm called robust discriminant analysis based on nonparametric maximum entropy (MaxEnt-RDA). By using robust radial basis function (RBF) kernels, KI-RDA can effectively deal with the data mixed with noise as well as the non-Gaussian distributed nonlinear data. Its robustness is accredited to that KI-RDA makes use of the kernel-induced non-Euclidean distance instead of the Euclidean distance in LDA to characterize the within-class and between-class divergence respectively. With the aid of these divergences, the paper defines a discriminant criterion which is similar to LDA for feature extraction, but this leads to a corresponding nonlinear optimization problem. With the further help of approximation strategy, the problem is converted into a generalized eigenvalue problem which can be solved directly so as to get a closed-form solution of the dimensionality reduction matrix. At last, experiments on multifold datasets verify the effectiveness of KI-RDA. Because of the diversity of kernel functions, KI-RDA is actually a general discriminant analysis framework.%提出了基于核诱导距离度量的鲁棒判别分析算法(robust discriminant analysis based on kernel-induced distance measure,KI-RDA).KI-RDA不仅自然地推广了线性判别分析(linear discriminant analysis,LDA),而且推广了最近提出的强有力的基于非参数最大熵的鲁棒判别分析(robust discriminant analysis based on nonparametric maximum entropy,MaxEnt-RDA).通过采用鲁棒径向基核,KI-RDA不仅能有效处理含噪数据,而且也适合处理非高斯分布的非线性数据,其本质的鲁棒性归咎于KI-RDA通过核诱导的非欧距离代替LDA的欧氏距离来刻画类间散度和类内散度.借助这些散度,为特征提取定义类似LDA的判别准则,导致了相应的非线性优化问题.进一步借助近似策略,将优化问题转化为直接可解的广义特征值问题,由此获得降维变换(矩阵)的闭合解.最后在多类数据集上进行实验,验证了KI-RDA的有效性.由于核的多样性,使KI-RDA事实上成为了一个一般性判别分析框架.