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

DOI10.1109/TSP.2016.2537272zbMATH Open1414.94576arXiv1508.01720OpenAlexW2198953102MaRDI QIDQ4619604

M. R. D. Rodrigues, Francesco Renna, Jure Sokolić, Robert Calderbank

Publication date: 7 February 2019

Published in: IEEE Transactions on Signal Processing (Search for Journal in Brave)

Abstract: This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes 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.

Full work available at URL: https://arxiv.org/abs/1508.01720

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)