Study On Bilateral-truncated-loss Based Robust Support Vector Machine Algorithm For Classification Problems

Support vector machine (SVM) is an important methodology for classification problemsand nonlinear function estimation problems in the fields of pattern recognition and machinelearning. One of the main drawbacks in the application of the standard SVM model is that itstraining process is sensitive to outliers or noises in the training dataset. In order to reduce theeffects of the outliers, Wang et al proposed a bilateral-weighted FSVM (BW-FSVM) model.However, high computational complexity limits the applications of BW-FSVM model inpractical classification problems. And it is a difficult task how to set reasonable fuzzyrelationship degrees of the training samples. The main researches and analyses on theseproblems can be classified as follows:1. SMO algorithm for bilateral-weighted fuzzy support vector machine classifier isproposed. The SMO algorithm was proposed to reduce the computational complexity of theBW-FSVM model, which firstly decomposes the overall quadratic program (QP) problem intothe smallest possible QP sub-problems and then solves these QP sub-problems analytically.Experiment results show that the proposed method is feasible and effective.2. A bilateral-truncated-loss based robust support vector machine (BTL-RSVM) modelfor classification problems with outliers or noises is proposed. The robustness of theBW-FSVM depends greatly on the fuzzy membership degrees of the training samples.However, it is very difficult to set reasonable fuzzy membership degrees for the trainingsamples. This paper outlines the construction of BTL-RSVM model for classificationproblems with outliers or noises and an algorithm is developed to solve the problem based onthe concave-convex procedure (CCCP).Theoretically, we discuss the relationship between theoptimal solutions of the BTL-RSVM model and the BW-FSVM model. A set of experimentsis conducted to test the robustness of the BTL-RSVM model. The results indicate thatcompared with the standard SVM model and the BW-FSVM model, BTL-RSVM modelreduces the effects of the outliers or noises and provides superior robustness.