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