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Manifold Learning for Multi-dimensional Auto-regressive Dynamical Models

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Machine Learning for Vision-Based Motion Analysis

Part of the book series: Advances in Pattern Recognition ((ACVPR))

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Abstract

We present a general differential-geometric framework for learning distance functions 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 automorphism. The problem of classifying motions, encoded as dynamical models of a certain class, can then be posed on the learnt manifold. In particular, we consider the class of multidimensional autoregressive models of order 2. Experimental results concerning identity recognition are shown that prove how such optimal pullback Fisher metrics greatly improve classification performances.

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Notes

  1. 1.

    In the case considered here, a single coordinate chart actually spans the whole manifold.

  2. 2.

    Here {V k+1} is a sequence of martingale increments and {W k+1} is a sequence of i.i.d. Gaussian noises \({\mathcal {N}}(0,1)\).

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Authors and Affiliations

    Authors
    1. Fabio Cuzzolin
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    Correspondence to Fabio Cuzzolin .

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    Editors and Affiliations

    1. Department of Computer Science, University of Bath, Bath, BA2 7AY, United Kingdom

      Liang Wang

    2. Dept. Electrical and Information Eng., University of Oulu, Oulu, 90014, Finland

      Guoying Zhao

    3. Bioinformatics Institute, A*STAR, 30 Biopolis Street, #07-01 Matrix, Singapore, 138671, Singapore

      Li Cheng

    4. Department of Electrical Engineering, Machine Vision & Media Processing Unit, University of Oulu, Oulu, Finland

      Matti Pietikäinen

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    © 2011 Springer-Verlag London Limited

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    Cuzzolin, F. (2011). Manifold Learning for Multi-dimensional Auto-regressive Dynamical Models. In: Wang, L., Zhao, G., Cheng, L., Pietikäinen, M. (eds) Machine Learning for Vision-Based Motion Analysis. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-0-85729-057-1_3

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    • DOI: https://doi.org/10.1007/978-0-85729-057-1_3

    • Publisher Name: Springer, London

    • Print ISBN: 978-0-85729-056-4

    • Online ISBN: 978-0-85729-057-1

    • eBook Packages: Computer ScienceComputer Science (R0)

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