Journal of Frontiers of Computer Science and Technology ›› 2012, Vol. 6 ›› Issue (9): 788-796.DOI: 10.3778/j.issn.1673-9418.2012.09.003

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Robust Discriminant Analysis Based on Kernel-Induced Measure

1. 南京航空航天大学 计算机科学与技术学院,南京 210016
2. 南京大学 计算机软件新技术国家重点实验室,南京 210093   

  1. 1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    2. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, China
  • Online:2012-09-01 Published:2012-09-03

核诱导距离度量的鲁棒判别分析

王嗣钧1+,陈松灿1,2   

  1. WANG Sijun1+, CHEN Songcan1,2

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