流形判别分析

Manifold-based Discriminant Analysis

传统降维方法主要有两种思路:一是利用样本的全局特征,保证降维前后样本的全局特征不变;二是尽量保证相邻样本在降维前后的相对关系不变。传统方法由于未能充分利用样本的已有信息,因此降维效率有限。鉴于此,在Fisher准则和局部流形保持的基础上,该文提出流形判别分析。该方法首先定义了基于流形的类内离散度MWCS和类间离散度MBCS,然后利用Fisher准则找到最佳投影方向,该方向满足MBCS与MWCS之比最大。该方法不仅继承了传统降维方法的优势,而且进一步提高了降维效率。标准数据集上的实验结果表明该文所提方法的有效性。

Researches on current Dimensionality Reduction （DR） methods are mainly based on two ways. One attempts to ensure the stabilities of global features of high-dimensional samples, the other tries to make the local manifold structure between data before and after dimension reduction be as invariant as possible. As the existed information is not fully utilized by current DR methods, the DR efficiencies are restricted. Based on the above analysis, Manifold-based Discriminnant Analysis （MDA） is proposed based on Fisher criterion and manifold preserving. The global features and local structure are both taken into consideration by MDA. It defines two scatters： Manifold-based Within-Class Scatter （MWCS） and Manifold-based Between-Class Scatter （MBCS）. According to Fisher criterion, the optimal projection satisfies the ratio of MBCS and MWCS is maximized. MDA not only inherits the superiorities of current DR methods, but further improves the DR efficiencies. Experiments on some standard datasets verify the effectiveness of the proposed method MDA.