%0 Journal Article
%T Single Directional SMO Algorithm for Least Squares Support Vector Machines
%A Xigao Shao
%A Kun Wu
%A Bifeng Liao
%J Computational Intelligence and Neuroscience
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/968438
%X Working set selection is a major step in decomposition methods for training least squares support vector machines (LS-SVMs). In this paper, a new technique for the selection of working set in sequential minimal optimization- (SMO-) type decomposition methods is proposed. By the new method, we can select a single direction to achieve the convergence of the optimality condition. A simple asymptotic convergence proof for the new algorithm is given. Experimental comparisons demonstrate that the classification accuracy of the new method is not largely different from the existing methods, but the training speed is faster than existing ones. 1. Introduction In a classification problem, we consider a set of training samples, that is, the input vectors along with corresponding class labels . Our task is to find a deterministic function that best represents the relation between input vectors and class labels. For classification or forecasting problems in machine learning, support vector machine (SVM) has been adopted in many applications because of its high precision [1¨C4]. SVMs require the solution of a quadratic programming problem. Another successful method for machine learning is least squares support vector machine (LS-SVM) [5]. Instead of solving a quadratic programming problem as in SVMs, the solutions of a set of linear equations are obtained in LS-SVMS. There are many proposed algorithms for training LS-SVMs: Suykens et al. proposed an iterative algorithm based on conjugate gradient (CG) algorithms [6]; Ferreira et al. presented a gradient system which can train the LS-SVM model [7] effectively; Chua introduced efficient computations for large least square support vector machine classifiers [8]; Chu et al. improved the efficiency of the CG algorithm by using one reduced system of linear equations [9]; Keerthi and Shevade extended the sequential minimal optimization (SMO) algorithms to solve the linear equations in LS-SVMs where the maximum violating pair (MVP) was selected as the working set [10]; based on the idea of SMO algorithm, Lifeng Bo et al. presented an improved method for working set selection by using functional gain (FG) [11]; Jian et al. designed a multiple kernel learning algorithm for LS-SVMs by convex programming [12]; and so on. These numerical algorithms are computationally attractive. Empirical comparisons show that SMO algorithm is more efficient than CG one for the large scale datasets. Fast SVM training speed with SMO algorithm is an important goal for practitioners and many other proposals have been given for this in the
%U http://www.hindawi.com/journals/cin/2013/968438/