Unsupervised Learning Using the Tensor Voting Graph

Abstract

Tensor Voting is a local, non parametric method that provides an efficient way to learn the complex geometric manifold structure under a significant amount of outlier noise. The main limitation of the Tensor Voting framework is that it is strictly a local method, thus not efficient to infer the global properties of complex manifolds. We therefore suggest constructing a unique graph which we call the Tensor Voting Graph, in which the affinity is based on the contribution of neighboring points to a point local tangent space estimated by Tensor Voting. The Tensor Voting Graph compactly and effectively represents the global structure of the underlying manifold. We experimentally demonstrate that we can accurately estimate the geodesic distance on complex manifolds, and substantially outperform all state of the art competing approaches, especially when outliers are present. We also demonstrate our method’s superior ability to segment manifolds, first on synthetic data, then on standard data sets for a motion segmentation, with graceful degradation in the presence of noise.