Manifold Partition Discriminant Analysis
提出一种新的监督降维算法MPDA，通过将数据流形划分为线性子空间并参数化切空间连接，同时考虑成对和高阶交互，以提升类内相似度度量并有效分离不同类别的邻近数据。
We propose a novel algorithm for supervised dimensionality reduction named manifold partition discriminant analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is consistent with the local variation of the data manifold, while nearby data belonging to different classes are well separated. By partitioning the data manifold into a number of linear subspaces and utilizing the first-order Taylor expansion, MPDA explicitly parameterizes the connections of tangent spaces and represents the data manifold in a piecewise manner. While graph Laplacian methods capture only the pairwise interaction between data points, our method captures both pairwise and higher order interactions (using regional consistency) between data points. This manifold representation can help to improve the measure of within-class similarity, which further leads to improved performance of dimensionality reduction. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.