A Curvature based Isometric Feature Mapping

Unsupervised metric learning consists in building adaptive distance functions without knowledge of the class labels to improve pattern classification. Usually, this process can be accomplished by manifold learning algorithms, through nonlinear dimensionality reduction. In this paper, we propose a curvature based Isometric Feature Mapping, a method that uses differential geometric concepts to build an intrinsic distance function that measures the variations of the local tangent spaces along shortest paths in the KNN graph, motivated by the Frenet-Serret equations and the notion of curvature. Experimental results with several real world datasets show that the proposed method is capable of producing classification performance comparable to other state-of-the-art dimensionality reduction based metric learning techniques, such as t-SNE and UMAP.