WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 7, 2012
Optimization of an SVM QP Problem Using Mixed Variable Nonlinear Polynomial Kernel Map and Mixed Variable Unimodal Functions
Authors: ,
Abstract: Support Vector Machines (SVM) can be constructed with the selection of an appropriate kernel function to solve an optimization problem. Algorithmic approaches can be taken to solve problems related to SVM which are used for regression analysis and data classiÖcation of a data set. The (inhomogeneous) polynomial kernel $$k (x, y) = (1 + x^{T}. y)^d$$ is useful for non-linear data set classiÖcation. In this work, the SVM QP problem with (inhomogeneous) polynomial kerne $$k (x, y)$$ is expressed as a mixed convex optimization problem with respect to the real variable $$ α \in \mathbb{R}^l$$ and $$ b \in \mathbb{R}$$, and the integer variable $$ d \in \mathbb{Z}$$. Several examples of mixed convexity and computational results are given. In addition, we introduce the deÖnitions of unimodal and semi-unimodal mixed variable functions with the corresponding minimization results
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Keywords: SVM, Inhomogeneous Polynomial Kernel Map, Unimodal Function, Mixed Convex Function, Minimization.