Semi-definite manifold alignment

Abstract

We study the problem of manifold alignment, which aims at "aligning" different data sets that share a similar intrinsic manifold provided some supervision. Unlike traditional methods that rely on pairwise correspondences between the two data sets, our method only needs some relative comparison information like "A is more similar to B than A is to C". This method provides a more flexible way to acquire the prior knowledge for alignment, thus is able to handle situations where corresponding pairs are hard or impossible to identify. We optimize our objective based on the graphs that give discrete approximations of the manifold. Further, the problem is formulated as a semi-definite programming (SDP) problem which can readily be solved. Finally, experimental results are presented to show the effectiveness of our method. © Springer-Verlag Berlin Heidelberg 2007.