Journal article Open Access

Linear Maximum Margin Classifier for Learning from Uncertain Data

Christos Tzelepis; Vasileios Mezaris; Ioannis Patras


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    <subfield code="u">Informatics and Telematics Institute, Centre for Research and Technology Hellas</subfield>
    <subfield code="a">Vasileios Mezaris</subfield>
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    <subfield code="u">School of Electronic Engineering and Computer Science, Queen Mary University of London</subfield>
    <subfield code="a">Christos Tzelepis</subfield>
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    <subfield code="a">Linear Maximum Margin Classifier for Learning from Uncertain Data</subfield>
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    <subfield code="a">&lt;p&gt;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.&lt;/p&gt;</subfield>
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