Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting

We address instance-based learning from a perceptual organization standpoint and present methods for dimensionality estimation, manifold learning and function approximation. Under our approach, manifolds in high-dimensional spaces are inferred by estimating geometric relationships among the input instances. Unlike conventional manifold learning, we do not perform dimensionality reduction, but instead perform all operations in the original input space. For this purpose we employ a novel formulation of tensor voting, which allows an N-D implementation. Tensor voting is a perceptual organization framework that has mostly been applied to computer vision problems. Analyzing the estimated local structure at the inputs, we are able to obtain reliable dimensionality estimates at each instance, instead of a global estimate for the entire data set. Moreover, these local dimensionality and structure estimates enable us to measure geodesic distances and perform nonlinear interpolation for data se...

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Philippos Mordohai, Gérard G. Medioni
• Keywords: Dimensionality, JMLR 2010, Manifold, Tensor Voting