Distance Approximating Dimension Reduction of Riemannian Manifolds

We study the problem of projecting high-dimensional tensor data on an unspecified Riemannian manifold onto some lower dimensional subspace1 without much distorting the pairwise geodesic distances between data points on the Riemannian manifold while preserving discrimination ability. Existing algorithms, e.g., ISOMAP, that try to learn an isometric embedding of data points on a manifold have a nonsatisfactory discrimination ability in practical applications such as face and gait recognition. In this paper, we propose a two-stage algorithm named tensor-based Riemannian manifold distance-approximating projection (TRIMAP), which can quickly compute an approximately optimal projection for a given tensor data set. In the first stage, we construct a graph from labeled or unlabeled data, which correspond to the supervised and unsupervised scenario, respectively, such that we can use the graph distance to obtain an upper bound on an objective function that preserves pairwise geodesic distances....

• Type: Journal
• Year: 2010
• Where: TSMC
• Authors: Changyou Chen, Junping Zhang, Rudolf Fleischer
• Keywords: Artificial Intelligence, Discrimination Ability, Manifolds, Pairwise Geodesic Distances, TSMC 2010