Data living on manifolds commonly appear in many applications. We show that under certain conditions, it is possible to construct an intrinsic and isometric data representation which respects the latent intrinsic manifold geometry. Namely, instead of learning the structure of the observed manifold, we view the observed data only as a proxy and learn the structure of a latent unobserved intrinsic manifold. We show successful application to unsupervised indoor localization in ad-hoc sensor networks.

This presentation is part of Minisymposium “MS53 - Dimensionality Reduction Algorithms for Large-Scale Images (2 parts)”
organized by: Salvatore Cuomo (Dept. Mathematics and Applications "Renato Caccioppoli", University of Naples) , Costantinos Siettos (National Technical University of Athens ) , Lucia Russo (Consiglio Nazionale delle Ricerche, Istituto di Ricerche sulla Combustione) .

Authors:

Ronen Talmon (Israel Institute of Technology)

Ariel Schwartz (Technion - Israel Institute of Technology)

Keywords:

data analysis, dimensionality reduction, kernel methods, localization, machine learning, manifold learning