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 capture 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.

中文翻译：

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流形分区判别分析

我们提出了一种新的有监督的降维算法，称为流形分割判别分析（MPDA）。它的目的是找到一个线性嵌入空间，沿着与数据流形的局部变化一致的方向实现类内相似度，同时将属于不同类的附近数据很好地分离。通过将数据流形划分为多个线性子空间并利用一阶泰勒展开，MPDA显式参数化切线空间的连接并以分段方式表示数据流形。虽然图拉普拉斯方法仅捕获数据点之间的成对交互，但我们的方法捕获数据点之间的成对和更高阶交互（使用区域一致性）。这种多方面的表示形式可以帮助改进类内相似度的度量，从而进一步提高降维性能。在多个真实数据集上的实验结果证明了该方法的有效性。