Nonparametric discriminant multi-manifold learning for dimensionality reduction

Based on that data sampled from the same class locate on one manifold and those labeled different classes reside on the corresponding manifolds, traditional data classification problem can be reasoned to multiply manifolds identification. Thus in this paper, a dimensionality reduction method titled nonparametric discirminant multi-manifold learning (NDML) is put forward and involved in different manifolds recognition. In the proposed method, a novel nonparametric manifold-to-manifold distance is defined to characterize the separability between manifolds. And then an objective function is modeled to project the original data into a low dimensional space, where the manifold-to-manifold distances can be maximized and manifolds locality will be preserved. Experiments have been carried out on benchmark face data sets with comparisons to some related dimensionality reduction methods such as Unsupervised Discriminant Projection (UDP), Constrained Maximum Variance Mapping (CMVM) and Linear Discriminant Analysis (LDA). The experimental results validate that the proposed NDML can obtain better performance than other methods.