An article written by Dr. Philippos Mordohai and Dr. Gérard Medioni entitled, 'Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting,' was recently accepted and published online by the Journal of Machine Learning Research.

Manifold learning is the process of estimating the structure and the number of degrees of freedom of an unknown system from a set of samples, also referred to as observations or instances.

For example, if one considers a set of observations that include the prices of real estate and other variables such as the ratio of residential to commercial properties, distances to employment centers and the average number of rooms per dwelling as points in a high-dimensional space, these points will not occupy the entire space, but are more likely to form a smooth hyper-surface in it.

Manifold learning would attempt to estimate the number of true degrees of freedom and to predict unknown prices based on similar observations.

This paper presents a method for manifold learning that addresses the problem from a perceptual organization point of view by extending tensor voting, a computational framework for perceptual organization, to high-dimensional spaces. This approach offers capabilities not found in current state of the art manifold learning methods and does not require global computations enabling parallel implementations and the processing of very large data sets. Results on numerous experiments on intrinsic dimensionality estimation, geodesic distance approximation and function approximation are shown in the paper.

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About the Journal of Machine Learning Research

The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online.

JMLR has a commitment to rigorous yet rapid reviewing. Final versions are published electronically (ISSN 1533-7928) immediately upon receipt. Until the end of 2004, paper volumes (ISSN 1532-4435) were published 8 times annually and sold to libraries and individuals by the MIT Press. Paper volumes (ISSN 1532-4435) are now published and sold by Microtome Publishing.