Multi-Class Learning: Simplex Coding And Relaxation Error
Author(s)Mroueh, Youssef; Poggio, Tomaso; Rosasco, Lorenzo; Slotine, Jean-Jacques E.
Center for Biological and Computational Learning (CBCL)
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We study multi-category classification in the framework of computational learning theory. We show how a relaxation approach, which is commonly used in binary classification, can be generalized to the multi-class setting. We propose a vector coding, namely the simplex coding, that allows to introduce a new notion of multi-class margin and cast multi-category classification into a vector valued regression problem. The analysis of the relaxation error be quantified and the binary case is recovered as a special case of our theory. From a computational point of view we can show that using the simplex coding we can design regularized learning algorithms for multi-category classification that can be trained at a complexity which is independent to the number of classes.
computational learning, machine learning, convex relaxation