Locality pursuit embedding

Abstract

Dimensionality reduction techniques are widespread in pattern recognition research. Principal component analysis, as one of the most popular methods used, is optimal when the data points reside on a linear subspace. Nevertheless, it may fail to preserve the local structure if the data reside on some nonlinear manifold, which is indisputably important in many real applications, especially when nearest-neighbor search is involved. In this paper, we propose locality pursuit embedding, a linear algorithm that arises by solving a variational problem. It produces a linear embedding that respects the local geometrical structure described by the Euclidean distances. Some illustrative examples are presented along with applications to real data sets.