Unsupervised Dimensionality Estimation and Manifold Learning in high-dimensional Spaces by Tensor Voting

Abstract

We address dimensionality estimation and nonlinear manifold inference starting from point inputs in high dimensional spaces using tensor voting. The proposed method operates locally in neighborhoods and does not involve any global computations. It is based on information propagation among neighboring points implemented as a voting process. Unlike other local approaches for manifold learning, the quantity propagated from one point to another is not a scalar, but is in the form of a tensor that provides considerably richer information. The accumulation of votes at each point provides a reliable estimate of local dimensionality, as well as of the orientation of a potential manifold going through the point. Reliable dimensionality estimation at the point level is a major advantage over competing methods. Moreover, the absence of global operations allows us to process significantly larger datasets. We demonstrate the effectiveness of our method on a variety of challenging datasets.