Research On Algorithm For Support Vector Machine Classifier

Support vector machine(SVM) arose in the middle of 1990's,and has become a focus of machine learning research in recent years.Since then,although just a period of about ten years,researchers have made great progress.SVM not only has solid theoretical foundation,but also wins universal commendation in practice.This technique is good both in theory and practice,and incomparable to any classic machine learning methods,its potential are encouraging! This dissertation studies the training of support vector machine with emphases on the sequential minimal optimization (SMO).The dissertation is arranged in five parts.The first part is introduction,including the studying background and the problems which will be solved in the dissertation.In the second part,the appearance and the summary of statistical learning theory are given.In the third part some definitions and conditions are presented to formulate the SVM training problem,which is described as a optimization problem.The primal optimization problem is first given for the case when all training data can be linearly separated.The primal optimization problem is studied from three aspects as follows. Judge it is the convex quadratic programming problem by some theories in the first aspect;In the second aspect its dual problem is worked out;The KKT condition is educed in the third aspect.By the same thought,the linearly inseparate SVM and the nonlinear SVM are studied.At last,the remarkable characteristic,the important thought and the application of SVM are introduced simply.In the fourth part,SMO algorithm is studied in detail,including the deducing process of the algorithm and the strategy of choosing two variables for every step in the sub-optimization problem.In the fifth part,the progress and the convergence of SMO algorithm are studied. When Gauss kernel function is adopted in SMO algorithm,the testing correctness of datasets is a bit low.For SVM,there are usually three kinds of kernel functions and by analysing the characteristics of these three functions,a combined kernel function,Gauss kernel function combining polynomial kernel function,is found.When the combined kernel function is adopted in SMO algorithm,the testing correctness of datasets is advanced.In this part the deducing process of the optimality condition of SVM dual problem and the proof to the convergence of SMO are also given.