Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple Kernel Learning (MKL) algorithms are based on the SVM large margin theory. Recently, SVMs have been analyzed from SVM and metric learning, and to develop new algorithms that build on the strengths of each. Inspired by the metric learning interpretation of SVM, we develop here a new metric-learning based SVM framework in which we incorporate metric learning concepts within SVM. We extend the optimization problem of SVM to include some measure of the within-class distance and along the way we develop a new within-class distance measure which is appropriate for SVM. In addition, we adopt the same approach for MKL and show that it can be also formulated as a Mahalanobis metric learning problem. Our end result is a number of SVM MKL algorithms that incorporate metric learning concepts. We experiment with them on a set of benchmark datasets and observe important predictive performance improvements.
Leading classification methods such as support vector machines (SVMs) and their counterparts achieve strong generalization performance by maximizing the margin of separation between data classes. While the maximum margin approach has achieved promising performance, this article identifies its sensitivity to affine transformations of the data and to directions with large data spread. Maximum margin solutions may be misled by the spread of data and preferentially separate classes along large spread directions. This article corrects these weaknesses by measuring margin not in the absolute sense but rather only relative to the spread of data in any projection direction. Maximum relative margin corresponds to a data-dependent regularization on the classification function while maximum absolute margin corresponds to an l2 norm constraint on the classification function. Interestingly, the proposed improvements only require simple extensions to existing maximum margin formulations and preserve the computational efficiency of SVMs. Through the maximization of relative margin, surprising performance gains are achieved on real-world problems such as digit, text classification and on several other benchmark data sets. In addition, risk bounds are derived for the new formulation based on Rademacher averages.