Manifold Alignment via Global and Local Structures Preserving PCA Framework

Abstract

Manifold alignment is very prevalent in machine learning for extracting common latent space from multiple datasets. These algorithms generally aim to achieve higher alignment accuracies by preserving the original structure while ensuring closeness between manifolds. This paper proposes a novel semi-supervised manifold alignment method that combines, in each manifold, both global and local linear reconstructions. We preserve a local structure through multiple manifold embedding methods. Moreover, we view manifold embedding methods as special forms of principal component analysis (PCA) and, thus, present a new penalty weight PCA approach to preserving a noise-free global structure. Finally, a closed-form solution is presented in the manifold alignment. This method can concurrently match the pair-wise correspondence and preserve both the global and local structures of each dataset to obtain a latent low-dimensional space. The extensive experiments on manifold alignment prove that the proposed method achieves significantly better alignment results than the comparative methods.