Stat841f09 - Wiki Course Notes

# Writing lagrangian form of support ve ctor m achine

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Unformatted text preview: s a discontinuity in the derivative. 2- norm or the Euclidean norm (the intuitive measure of the length of a vector), is easier to work with - that is . F or convenience, we will maximize where the constant 1/2 has been added for simplification and that the maximizing the function is the same as maximizing the square root of that function. This is an example of a quadratic programming problem and we will minimize a quadratic function subject to linear inequality constraints. Writing Lagrangian Form of Support Ve ctor M achine The Lagrangian form is introduced to ensure that the optimization conditions are satisfied, as well as finding an optimal solution (the optimal saddle point of the Lagrangian for the classic quadratic optimization). The problem will be solved in dual space by introducing as dual constraints, this is in contrast to solving the problem in primal space as function of the betas. A simple algorithm (http://www.cs.wisc.edu/dmi/lsvm/) for iteratively solving the Lagrangian has been found to run well on very large data sets, making SVM more usable. Note that this algorithm is intended to solve Support Vector Machines with some tolerance for errors - not all points are necessarily classified correctly. Several papers by Mangasarian explore different algorithms for solving SVM. . To find the optimal value, set the derivative equal to zero. , . Note that is equivalent to the constraints First, . wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 61/74 10/09/2013 Stat841 - Wiki Cour se Notes . . So this simplifies to . In other words, , Similarly, . This allows us to rewrite the Lagrangian without . . Because , and is constant, . So this simplifies further, to A dual representation of the maximum margin. Because is the Lagrange multiplier, . This is a much simpler optimization problem Exte ns ion:Global Optimization of Support Ve ctor M achine s (Us ing Ge ne tic Algorithms for Bankruptcy Pre diction) One of the most important research issues in finance is building accurate corporate bankruptcy prediction...
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## This document was uploaded on 03/07/2014.

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