Nonparametric discriminant multi-manifold learning

Abstract

In this paper, a nonparametric discirminant multi-manifold learning (NDML) method is presented for dimensionality reduction. Based on the assumption that the data with same label locate on the same manifold and those belonging to varied classes are resided on the corresponding manifolds, the traditional classification problem can be deduced to multi-manifold identification in low dimensional space. So this paper presents a discriminant learning algorithm to distinguish different manifolds, where a novel nonparametric manifold-to-manifold distance is defined. Moreover, an optimization function is modeled to explore a subspace with maximum manifold-to-manifold distances and minimum locality preserving. Experiments on AR face data and YaleB face data validate that NDML is of better performance than some other dimensionality reduction methods, such as Unsupervised Discriminant Projection (UDP), Constrained Maximum Variance Mapping (CMVM) and Linear Discriminant Analysis (LDA). © 2014 Springer International Publishing Switzerland.