Learning Geodesic Metric for Out-of-Sample Extension of Isometric Embedding

Geodesic distance calculation is a crucial stage in the distance-based manifold learning algorithms. Owning to the nonparametric of Isomap, however, it is not economic and convenient to compute the geodesic distances for an unseen new sample via neighborhood graph. In this paper, we proposed a geodesic metric learning (GML) scheme based on iterative majorization, to obtain a parametric geodesic metric function. Once the parametric geodesic metric is produced, one can calculate the geodesic distance directly and have no longer use for reconstructing the neighborhood graph for those unseen samples. Integrating distance-based triangulation with the parametric geodesic metric, it is easy to accomplish the task of feature extraction based on geodesic distance. Experiments on benchmark database have demonstrated the encouraged results