Local Learning Projections

Abstract

This paper presents a Local Learning Projection (LLP) approach for linear dimensionality reduction. We first point out that the well known Principal Component Analysis (PCA) essentially seeks the pro jection that has the minimal global estimation error. Then we propose a dimensionality reduction algorithm that leads to the pro jection with the minimal local estimation error, and elucidate its advantages for classification tasks. We also indicate that LLP keeps the local information in the sense that the pro jection value of each point can be well estimated based on its neighbors and their pro jection values. Experimental results are provided to validate the effiectiveness of the proposed algorithm.