Analysis Of Support Vectort Regression Machine Based On Noise Model

The statistical learning is a theory which research statistical learning rule at small sample situation. Based on this theory, Vapnik and coworkers develop SVM which is a very good and general learning machine in 1990s. SVM is widely used in pattern recognition, regression, estimation, function approximation, density estimation, etc.This paper from support vector machine in the application perspective of regression estimation, how to establish support vector regression machine which deal with noise data by selecting optimal loss function. This paper main works are as follows:1. The support vector regression machine of based on noise modelWhen the data is influenced by the noise, we construct support vector regression machine of based on noise model by combining not sensitive loss function and the introduction of noise model. We prove the solution of original problem of the support vector regression machine of based on noise model which is existence and uniqueness, and infer dual problem, also prove the existence of solutions of dual problem. Finally establish the support vector regression machine of based on noise model.2. The fuzzy support vector regression machine of based noise modelWhen the data is not only influenced by the noise, some data is fuzzy. Based on the fuzzy mathematics theory, we construct the fuzzy support regression machine of based on noise model. Firstly, brief introduction of the theory of fuzzy mathematics to prepare, combined with preparation with fuzzy mathematic theory and previous chapter of the support vector machine regression machine of based noise model, given the original problem of the fuzzy support vector regression machine of based noise model, and infer its dual problem. At last we extend the linear fuzzy support vector machine to nonlinear fuzzy support vector regression machine by introducing the kernel function.