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Learning Pullback Metrics for Linear Models

Abstract : In this paper we present an unsupervised differential-geometric approach for learning Riemannian metrics for dynamical models. Given a training set of models the optimal metric is selected among a family of pullback metrics induced by the Fisher information tensor through a parameterized diffeomorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then be posed on the learnt manifold. Experimental results concerning action and identity recognition based on simple scalar features are shown, proving how learning a metric actually improves classification rates when compared with Fisher geodesic distance and other classical distance functions.
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https://hal.inria.fr/inria-00326722
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Submitted on : Sunday, October 5, 2008 - 12:44:48 PM
Last modification on : Monday, October 6, 2008 - 9:40:12 AM
Long-term archiving on: : Monday, October 8, 2012 - 1:56:46 PM

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  • HAL Id : inria-00326722, version 1

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Fabio Cuzzolin. Learning Pullback Metrics for Linear Models. The 1st International Workshop on Machine Learning for Vision-based Motion Analysis - MLVMA'08, Oct 2008, Marseille, France. ⟨inria-00326722⟩

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