基于语境距离度量的拉普拉斯最大间距判别准则

线性拉普拉斯判别准则(Linear Laplacian discrimination, LLD)作为一种非线性特征提取方法得到了较为成功的运用. 然而通过分析得知在具体使用LLD方法的过程中还会面临小样本以及如何确定原始样本空间类型的问题. 因此, 本文引入语境距离度量并结合最大间距判别准则的基本原理提出一种基于语境距离度量的拉普拉斯最大间距判别准则(Contextual-distance metric based Laplacian maximum margin criterion, CLMMC). 该准则不但在一定程度上避免小样本问题, 而且由于语境距离度量更关注输入样本簇内在的本质结构而不是原始样本空间的类型, 从而降低了该准则对特定样本空间的依赖程度. 同时通过引入计算语境距离度量的新算法并结合QR分解的基本原理, 使得CLMMC在处理高维矢量模式数据时更具适应性和效率. 并从理论上讨论CLMMC准则具有的基本性质以及与LLD准则的内在联系. 实验证明CLMMC准则具有上述优势.

Contextual-distance Metric Based Laplacian Maximum Margin Criterion

Linear Laplacian discrimination (LLD) as a non-linear feature extraction method has obtained very extensive applications. However, LDD suffers from the small sample size problem (SSS) and/or the type of the sample space when it is used. In order to circumvent such shortcomings, a contextual-distance metric based Laplacian maximum margin criterion (CLMMC) is proposed in this paper by using contextual-distance metric and integrating maximum margain criterion (MMC) into the LLD. The proposed criterion can obviously decrease the dependence on the sample space since the contextual-distance metric focuses more on intrinsic structure of a cluster of samples than on its type. And it is of higher adaptability and efficiency to use the new algorithm to compute contextual-distance metric and applying QR-discomposition when high-dimensional vector data are dealt with. The basic properties of CLMMC and its relation to LLD are also discussed. The experimental results indicate the above advantages of the CLMMC.