线性子空间分类中的不匹配：可靠分类的充分条件
Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification
摘要：
本文研究了具有不匹配分类器的线性子空间的分类问题。特别是，我们假设一个模型，其中一个观察信号中存在的各向同性高斯噪声和信号的分布条件下，一个给定的类是高斯与零均值和低秩协方差矩阵。我们还假设分类器只知道输入分布参数的不匹配版本，而不是真正的参数。通过构建这样一个不匹配的分类器的错误概率的上限的渐近低噪声扩展，我们提供了足够的条件，在低噪声制度，能够急剧预测的分类错误地板的情况下，可靠的分类。这样的条件是真实信号分布的几何形状、失配信号分布的几何形状以及这样的几何形状之间的相互作用（即，真实信号子空间和失配信号子空间之间的主要角度和重叠）的函数。数值结果表明，我们的条件，可靠的分类可以很好地预测一个不匹配的分类器的行为与合成数据和运动分割和手写数字分类应用。
英文摘要：
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.
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