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Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

Sokolic, J; Renna, F; Calderbank, R; Rodrigues, MRD; (2016) Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification. IEEE Transactions on Signal Processing , 64 (12) pp. 3035-3050. 10.1109/TSP.2016.2537272. Green open access

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Abstract

signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.

Type: Article
Title: Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2016.2537272
Publisher version: http://doi.org/10.1109/TSP.2016.2537272
Language: English
Additional information: Open Access article. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Classification, mismatch, linear subspace, maximum-a-posteriori classifier, error floor
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1529580
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