LAUSR

In recent years, manifold alignment methods have aroused a great of interest in the machine learning community which construct a common latent space shared by multiple input data sets. In a semi-supervised problem, it is assumed that some predetermined correspondences are available to us. The effectiveness of the semi-supervised manifold alignment methods may be very limited with very limited prior information. In this paper, we propose a novel semi-supervised manifold alignment algorithm with few given pairwise correspondences. Our approach characterizes the manifold structure of each sample point using the geodesic distances between the sample point and given correspondences. Then we build the connections between the points sampled different manifolds using the characterized manifold structure. The points of multiple data sets are finally projected to a common space simultaneously preserving the local geometry of each manifold and the captured connections between manifolds. We demonstrate the effectiveness of our method in a series of carefully designed experiments.