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

• Published in: IEEE transactions on signal processing Vol. 64; no. 12; pp. 3035 - 3050
• Main Authors: Sokolic, Jure, Renna, Francesco, Calderbank, Robert, Rodrigues, Miguel R. D.
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.06.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Classification; Computer vision; Covariance matrices; error floor; Error probability; Geometry; linear subspace; maximum-a-posteriori classifier; mismatch; Motion segmentation; Noise; Normal distribution; Reliability; Upper bound
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2016.2537272

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.