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.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence. (c)
2017 IEEE. DOI: 10.1109/TPAMI.2017.2772235 Author's accepted version. The
final publication is available at
http://ieeexplore.ieee.org/document/8103808