Abstract
A new general dimension reduction framework based on similar and dissimilar metric learning is proposed in this paper which allows us to exploit the geometry of data to reduce the data dimension for classification and visualization. The general formulation can unify the existing dimension reduction algorithms within a common framework. Furthermore, this metric learning framework can be used as a general platform for developing new dimension reduction algorithms. By utilizing this framework as a tool, we propose a novel supervised dimension reduction algorithm named sub-manifold preserving analysis (SMPA) in which the intrinsic sub-manifold structure will be preserved while the margin of interclass will be separated. Experimental evidences show that performance of our proposed SMPA algorithm is better than other algorithms.