In this paper, we propose a maximum margin classifier that deals with
uncertainty in data input. More specifically, we reformulate the SVM framework
such that each training example can be modeled by a multi-dimensional Gaussian
distribution described by its mean vector and its covariance matrix -- the
latter modeling the uncertainty. We address the classification problem and
define a cost function that is the expected value of the classical SVM cost
when data samples are drawn from the multi-dimensional Gaussian distributions
that form the set of the training examples. Our formulation approximates the
classical SVM formulation when the training examples are isotropic Gaussians
with variance tending to zero. We arrive at a convex optimization problem,
which we solve efficiently in the primal form using a stochastic gradient
descent approach. The resulting classifier, which we name SVM with Gaussian
Sample Uncertainty (SVM-GSU), is tested on synthetic data and five publicly
available and popular datasets; namely, the MNIST, WDBC, DEAP, TV News Channel
Commercial Detection, and TRECVID MED datasets. Experimental results verify the
effectiveness of the proposed method.

本文提出一种最大间隔分类器 SVM-GSU，使用多维高斯分布描述每个训练样本，以处理数据输入中的不确定性，并使用随机梯度下降方法高效地解决凸优化问题。通过测试，证明该方法的有效性。