Non-linear Metric Learning Using Metric Tensor

Abstract

Manifold based metric learning methods have become increasingly popular in recent years. In almost all these methods, however, the underlying manifold is approximated by a point cloud, and the matric tensor, which is the most basic concept to describe the manifold, is neglected. In this paper, we propose a non-linear metric learning framework based on metric tensor. We construct a Riemannian manifold and its metric tensor on sample space, and replace the Euclidean metric by the learned Riemannian metric. By doing this, the sample space is twisted to a more suitable form for classification, clustering and other applications. The classification and clustering results on several public datasets show that the learned metric is effective and promising.