A Study And Application Of Weighted Fuzzy Support Vector Classifiers Based On Posteriori Probability

Support Vector Machine is a new tool to solve the problem of machine learning by the use of optimization method. SVM can be successful to deal with regression problems, classification problem and many other problems. Fuzzy support vector machine(FSVM), as a deformation of SVM, is proposed to solve the problem that SVM is sensitive to outliers and noises in the training set. However, traditional methods of fuzzy support vector machine to determine the fuzzy membership of samples do not really reflect the role of samples in building separating hyperplane. And determine the fuzzy memberships are based on the original space. At the same time the generalization ability of FSVM will be affected by the training parameters.The paper mainly researches the establishment of membership function and parameters optimization of FSVC. The main researches include:(1)Firstly we research the detection methods of outliers in the data sets. Because samples in the original space will be re-distributed in the feature space, It is more accurate that we detect Outliers in feature space which FSVC is trained in. We introduce the concept of feature space to the method of outliers Detection based on Average Density, and setup the method of outliers Detection based on Average Density in feature space. The improved method of the outliers detecting detects the outliers in feature space. So we obtain the real outliers.(2)Traditionally, the methods that define the membership of samples weaken the role of support vector in building separating hyperplane when it weakens the role of outliers and noise points. In this paper, we propose a Weighted Fuzzy Support Vector Classifiers Based on Posteriori Probability. The improved membership function can efficiently diminish the outliers and noise samples'role in building separating hyperplane. At the same time, it do not reduce the support vectors'role of in building separating hyperplane.The anti-noise ability of SVC is improved. Then considering that samples in the original space will be re-distributed in the feature space, the improved membership function calculates the membership of samples in the feature space. (3)The traditional methods of select parameters of SVM are slow and the results fall into local optimal solution. The improved Particle Swarm Optimization algorithm which is based on the combination of selection and crossover operations in genetic strategy is adopted to select parameters of FSVC. The improved PSO improve the algorithm performance by linear time-varying inertia weight. The improved PSO introduce selection and crossover operations in genetic strategy to enhance the excellent characteristics of particles So that particles can jump out of local optimum. At the same time to speed up the convergence rate.Finally, we simulate on above methods. The experimental results show that the weighted fuzzy support vector Classifiers based on posteriori probability is better than the traditional fuzzy support vector Classifiers in the ability of anti-noise and classification. The improved PSO can search in a larger space more quickly and effectively. It has a greater advantage on searching speed and sparsity and is able to find the global optimal solution quickly and accurately. .