Matrix exponential based semi-supervised discriminant embedding for image classification

Abstract

Semi-supervised Discriminant Embedding (SDE) is the semi-supervised extension of Local Discriminant Embedding (LDE). Since this type of methods is in general dealing with high dimensional data, the small-sample-size (SSS) problem very often occurs. This problem occurs when the number of available samples is less than the sample dimension. The classic solution to this problem is to reduce the dimension of the original data so that the reduced number of features is less than the number of samples. This can be achieved by using Principle Component Analysis for example. Thus, SDE needs either a dimensionality reduction or an explicit matrix regularization, with the shortcomings both techniques may suffer from. In this paper, we propose an exponential version of SDE (ESDE). In addition to overcoming the SSS problem, the latter emphasizes the discrimination property by enlarging distances between samples that belong to different classes. The experiments made on seven benchmark datasets show the superiority of our method over SDE and many state-of-the-art semi-supervised embedding methods.