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Multi-Class Learning: Simplex Coding And Relaxation Error

Author(s)
Mroueh, Youssef; Poggio, Tomaso; Rosasco, Lorenzo; Slotine, Jean-Jacques E.
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DownloadMIT-CSAIL-TR-2011-043.pdf (209.8Kb)
Other Contributors
Center for Biological and Computational Learning (CBCL)
Advisor
Tomaso Poggio
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Abstract
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.
Date issued
2011-09-27
URI
http://hdl.handle.net/1721.1/66085
Series/Report no.
MIT-CSAIL-TR-2011-043CBCL-305
Keywords
computational learning, machine learning, convex relaxation

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