| Support Vector Machine (SVM) is a machine learning method based on statistical learning theory.Because it resolves the small sample, nonlinearity, high dimension and local minimum problemsperfectly and has good generalization ability, SVM has been a hot field of machine learning.However, tradition SVM is very sensitive to noises and outliers in the training sample, in order toovercome this problem, the fuzzy support vector machine (FSVM) is proposed. It is how toconstruct a suitable membership function that has been the primary problem in FSVM. In addition,how to promote FSVM from the geometry aspect has became another hot topic.This dissertation has elaborated the theory, algorithm and properties of SVM. The theory andalgorithm of FSVM perform more perfectly by constructing an appropriate membership function,kernel function and improving geometry of FSVM. After conducting a research deep into this topic,the main results are as follows:(1) Using the dynamic kernel function, which is constructed from information geometry aspect,to express the distance between sample points and their cluster centers and the affinity among thesample points, that is to say, the kernel method is introduced to the representation of distance andaffinity;(2) The product of combined fuzzy classification and regression membership function based onthe cluster center and the affinity are proposed. They are defined not only the distance between apoint and its cluster center, but also two different points of the sample, which is depicted as theaffinity between them;(3) L-2 norm fuzzy support vector regression is proposed from the geometry aspect. Thesimulation results show that it has better regression accuracy than support vector regression and L-1norm fuzzy support vector regression;(4) The algorithms of fuzzy support vector classification and fuzzy support vector regressionbased on information geometry are proposed. Then the fuzzy support vector classification algorithmis used to extract the edge of image. |
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