Regularized least squares locality preserving projections with applications to image recognition.

Abstract

Locality preserving projection (LPP), as a well-known technique for dimensionality reduction, is designed to preserve the local structure of the original samples which usually lie on a low-dimensional manifold in the real world. However, it suffers from the undersampled or small-sample-size problem, when the dimension of the features is larger than the number of samples which causes the corresponding generalized eigenvalue problem to be ill-posed. To address this problem, we show that LPP is equivalent to a multivariate linear regression under a mild condition, and establish the connection between LPP and a least squares problem with multiple columns on the right-hand side. Based on the developed connection, we propose two regularized least squares methods for solving LPP. Experimental results on real-world databases illustrate the performance of our methods.