Manifold Alignment Based on Sparse Local Structures of More Corresponding Pairs

Abstract

Manifold alignment is to extract the shared latent semantic structure from multiple manifolds. The joint adjacency matrix plays a key role in manifold alignment. To construct the matrix, it is crucial to get more corresponding pairs. This paper proposes an approach to obtain more and reliable corresponding pairs in terms of local structure correspondence. The sparse reconstruction weight matrix of each manifold is established to preserve the local geometry of the original data set. The sparse correspondence matrices are constructed using the sparse local structures of corresponding pairs across manifolds. Further more, a new energy function for manifold alignment is proposed to simultaneously match the corresponding instances and preserve the local geometry of each manifold. The shared low dimensional embedding, which provides better descriptions for the intrinsic geometry and relations between different manifolds, can be obtained by solving the optimization problem with closed-form solution. Experiments demonstrate the effectiveness of the proposed algorithm.