Manifold Partition Discriminant Analysis

TL;DR

Manifold Partition Discriminant Analysis (MPDA) is a new supervised dimensionality reduction technique that partitions data manifolds into linear subspaces to better preserve class structure and improve data embedding quality.

Contribution

The paper introduces MPDA, a novel manifold partitioning approach that explicitly models local tangent spaces and captures higher-order interactions for enhanced dimensionality reduction.

Findings

MPDA outperforms existing methods on multiple datasets.

It effectively captures local manifold structures.

The method improves class separation in reduced dimensions.

Abstract

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.