Extensions of Manifold Learning Algorithms in Kernel Feature Space

Yaoliang Yu, Peng Guan, Liming Zhang

Abstract: Manifold learning algorithms have been proven to be capable of discovering some nonlinear structures. However, it is hard for them to extend to test set directly. In this paper, a simple yet effective extension algorithm called PIE is proposed. Unlike LPP, which is linear in nature, our method is nonlinear. Besides, our method will never suffer from the singularity problem while LPP and KLPP will. Experimental results of data visualization and classification validate the effectiveness of our proposed method.