Fuzzy Support Vector Machine

Support vector machine is a pattern recognization method based on statistical learning theory, is the hotspot of machine learning. With its theory and algorithm consummated, it has become the powerful tool of machine learning. In machine learning, always suppose all samples come from an unknown distribution with equal chance. But, in some question, each sample has different confidence for the question, which request give the sample has bigger confidence more attention and limit the function of the sample whose confidence smaller. Aimming at this fact, inspired by Data Domain Description Based on Fuzzy Support Vector Machines by Wei and Fuzzy Support Vector Machine by Lin. In this paper, constituted four fuzzy support vector models by controling the influence of each sample on the learning machine by its confidence, the sample who has begger confidence has bigger function on the learning machine, the one who has smaller confidence has smaller function or no function on the learning machine. Fistly, constituted fuzzy support vector classification geometrical model based on geometrical support vector classification. Compare to the fuzzy support vector classification model by Lin, this model could more embody the difference of the confidence of each sample. Secondly, constituted fuzzy support vector regression model and fuzzy support vector regression geometrical model. Numerical analysis testified the fuzzy support vector regression could more embody the difference of confidence to fuzzy support vector regression geometrical model. But fuzzy support vector regression is more complexity and has bigger compution. Thirdly, aimming at the support vector machine explanation of principal component analysis based on Structural Risk Minimization, constituted the fuzzy principal component analysis model which be applicable to the samples with different confidence. Numerical analysis testified that these fuzzy models can effectively control the influence of each sample on learning machine according to its confidence.