Local Learning Pro jections

Local Learning Pro jections
Mingrui Wu - Max Planck Institute for Biological Cybernetics, Germany Kai Yu - NEC Labs America, USA Shipeng Yu - Siemens Medical Solutions, USA Bernhard Schölkopf - Max Planck Institute for Biological Cybernetics, Germany
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.

Mingrui Wu - Max Planck Institute for Biological Cybernetics, Germany
Kai Yu - NEC Labs America, USA
Shipeng Yu - Siemens Medical Solutions, USA
Bernhard Schölkopf - Max Planck Institute for Biological Cybernetics, Germany

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.