Title :
Exterior-Point Method for Support Vector Machines
Author :
Bloom, Victoria ; Griva, Igor ; Byong Kwon ; Wolff, Anna-Rose
Author_Institution :
Sch. of Phys., Astron. & Comput. Sci., George Mason Univ., Fairfax, VA, USA
Abstract :
We present an exterior-point method (EPM) for training dual-soft margin support vector machines (SVMs). The EPM stems from nonlinear rescaling and augmented Lagrangian methods and allows iterates to approach the solution of a constrained nonlinear optimization problem from the exterior of the feasible set. Furthermore, the EPM produces and solves a well-conditioned system of linear equations at each iteration; thus, avoiding numerical inaccuracies that can occur when solving ill-conditioned systems. Therefore, the EPM may be an attractive alternative to existing quadratic programming solvers for training SVMs. We report numerical results for training the SVM with the EPM on data up to several thousand data points from the UC Irvine Machine Learning Repository.
Keywords :
iterative methods; learning (artificial intelligence); nonlinear programming; support vector machines; EPM stems; SVMs; UC Irvine machine learning repository; augmented Lagrangian methods; constrained nonlinear optimization problem; dual-soft margin support vector machine training; exterior-point method; ill-conditioned systems; iteration; linear equations; nonlinear rescaling; support vector machines; well-conditioned system; Approximation algorithms; Kernel; Optimization; Support vector machines; Training; Training data; Vectors; Augmented Lagrangian (AL); exterior-point method (EPM); nonlinear rescaling (NR); quadratic optimization; supervised learning; support vector machine (SVM); support vector machine (SVM).;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2013.2288101