Manifold Alignment Based on Sparse LocalStructures of More Corresponding Pairs.

Abstract

Manifold alignment is to extract the shared latentsemantic structure from multiple manifolds. Thejoint adjacency matrix plays a key role in mani-fold alignment. To construct the matrix, it is cru-cial to get more corresponding pairs.This pa-per proposes an approach to obtain more and re-liable corresponding pairs in terms of local struc-ture correspondence.The sparse reconstructionweight matrix of each manifold is established topreserve the local geometry of the original dataset. The sparse correspondence matrices are con-structed using the sparse local structures of corre-sponding pairs across manifolds. Further more, anew energy function for manifold alignment is pro-posed to simultaneously match the correspondinginstances and preserve the local geometry of eachmanifold. The shared low dimensional embedding,which provides better descriptions for the intrin-sic geometry and relations between different man-ifolds, can be obtained by solving the optimizationproblem with closed-form solution. Experimentsdemonstrate the effectiveness of the proposed algo-rithm.