Manifold-based Discriminant Analysis

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.