This paper introduces a geometrically inspired large-margin classifier that can be a better alternative to the Support Vector Machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls, which may be unrealistically tight in high-dimensional spaces. To find the best separating hyperplane between any pair of classes approximated with the affine hulls, we first compute the closest points on the affine hulls and connect these two points with a line segment. The optimal separating hyperplane is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. To allow soft margin solutions, we first reduce affine hulls in order to alleviate the effects of outliers and then search for the best separating hyperplane between these reduced models. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed method compares favorably with the SVM classifier.
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