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.
Highlights
S IGNAL classification is a fundamental task in various fields, including statistics, machine learning and computer vision
Our goal is to study the performance of the MMAP classifier by establishing conditions, which are a function of the geometry of the true and mismatched signal models as well as the interaction of such geometries, for reliable classification in the low-noise regime i.e., such that
The expansion of the upper bound to the error probability embodied in Theorem 2 provides a set of conditions, which are a function of the geometry of the true signal model, the geometry of the mismatched signal model, and the interaction of the geometries, that enable us to understand whether or not the upper bound to the error probability may exhibit an error floor
Summary
S IGNAL classification is a fundamental task in various fields, including statistics, machine learning and computer vision. One often approaches this problem by leveraging the Bayesian inference paradigm, where one infers the signal class from signal samples or measurements based on a model of the joint distribution of the signal and signal classes ([1], Chapter 2). The associate editor coordinating the review of this manuscript and approving it for publication was Prof. This paper was presented in part at the IEEE International Symposium on Information Theory 2015
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