Multi-Class Learning: Simplex Coding And Relaxation Error
Name
MIT-CSAIL-TR-2011-043.pdf
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209.83 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Mroueh, Youssef
Poggio, Tomaso
Rosasco, Lorenzo
Slotine, Jean-Jacques E.
Advisor(s)
Tomaso Poggio
Date Issued
September 27, 2011
Series/Report no.
MIT-CSAIL-TR-2011-043
CBCL-305
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.
Subjects
computational learning
machine learning
convex relaxation
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