DEMING ZHAI et al.: MANIFOLD ALIGNMENT VIA CORRESPONDING PROJECTIONS 1 Manifold Alignment via Corresponding Projections

In this paper, we propose a novel manifold alignment method by learning the underlying common manifold with supervision of corresponding data pairs from different observation sets. Different from the previous algorithms of semi-supervised manifold alignment, our method learns the explicit corresponding projections from each original observation space to the common embedding space everywhere. Benefiting from this property, our method could process new test data directly rather than re-alignment. Furthermore, our approach doesn’t have any assumption on the data structures, thus it could handle more complex cases and get better results compared with previous work. In the proposed algorithm, manifold alignment is formulated as a minimization problem with proper constraints, which could be solved in an analytical manner with closed-form solution. Experimental results on pose manifold alignment of different objects and faces demonstrate the effectiveness of our proposed method.