Abstract: 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.

Key words: dimensionality reduction, discriminant analysis, kernel-induced distance, robustness

摘要： 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。

关键词: 降维, 判别分析, 核诱导的距离, 鲁棒性