Optimal Dimentionality of Metric Space for Classification

by Wei Zhang, Xiangyang Xue, Zichen Sun, Yue-Fei Guo and Hong Lu

This is an ICML 2007 paper. After reading it, I found nothing really astonishing. However it gives another direction of research. The idea is based on one of the papers I read long ago, LPP. The technique of LPP is based on Laplacian Eigenmap by finding a linear transform that minimize a similar object function as Laplacian Eigenmap. However, they are both unsupervised learning techniques.

This paper however, when the Laplacian matrix is constructed, supervised information is incorporated by setting a positive value for samples of the same class, 0 for too far away samples and a negative value for samples of different classes.

Then the so-called optimal projection uses the eigen vectors of negative eigenvalues. Though the idea is simple and direct, it works anyway and the experiment and analysis are both detailed and convincing.