Manifold alignment using curvature information

Manifold learning (ML) is a known non-linear technique for representing high dimensional data. Despite the potential power of ML techniques, they fail in representing an unseen test data accurately. To better model the geometric structure of manifolds, Manifold Alignment (MA) techniques have been proposed recently, where the majority of these algorithms rely on point correspondences between two manifolds. However having such knowledge is not applicable in many real world applications. This paper proposes to extract the intrinsic geometric information of manifolds and utilize it to align two manifolds. The proposed algorithm utilizes the multiscale singular value decomposition technique to estimate the high dimensional curvature of data and apply to iteratively align two manifolds. To evaluate the efficiency of the proposed method, visual object registration and image recognition applications are studied. Our experimental results demonstrate that employing curvature information for manifold alignment improves the accuracy of both the registration and recognition results.