Mathematical Programming in Data Mining

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ABSTRACT0138308Olvi MangssarianU of Wisconsin-MadisonSupport vector machines (SVMs) have played a key role in broad classes of problems arising in various fields. Much more recently, SVMs have become the tool of choice for problems arising in data mining. This proposal de-scribes some aspects of support vector machines that the proposer would like to study and contribute further to. These include: generalized SVMs (a gen-eral mathematical programming framework for SVMs), unconstrained SVMs (a strongly convex minimization reformulation of SVMs solvable by a fastfinite method), Lagrangian classification (an unconstrained Lagrangian rep-resentation of SVMs leading to an extremely simple iterative scheme capable of solving classification problems with millions of data points) and reduced data classification (a rectangular kernel classifier that is characterized by as little as 1% of the data).