Linear Maximum Margin Classifier for Learning from Uncertain Data

In this paper, we propose a maximum margin classifier that deals with uncertainty in data input. Specifically, we reformulate the SVM framework such that each input training entity is not solely a feature vector representation, but a multi-dimensional Gaussian distribution with given probability density, i.e., with a given mean and covariance matrix. The latter expresses the uncertainty. We arrive at a convex optimization problem, which is solved in the primal form using a gradient descent approach. The resulting classifier, which we name SVM with Gaussian Sample Uncertainty (SVM-GSU), is tested on synthetic data, as well as on the problem of event detection in video using the large-scale TRECVID MED 2014 dataset, and the problem of image classification using the MNIST dataset of handwritten digits. Experimental results verify the effectiveness of the proposed classifier.