Robustness Of Fuzzy Classification And Fuzzy RMM One-class Classifier

Statistical learning theory which is developed in recent years is an important branch of machine learning, most of the effective learning algorithm of statistical learning are based on risk minimization theory, including SVM, Kernel function methods, Logistic regress, Least Squares regress and so on. Compared with other machine learning methods, these methods possess good performance, therefore, they are widely applied in data classification, pattern recognition, data mining. It is important to investigate influence of data perturbation on classification machine, namely robustness properties for classification algorithms, because statistical learning needs to obtain the parameter of classification machine from limited small sample, On the other hand, maximize the absolute boundary is the starting point of many classification methods , including SVM. Some defects of the methods can be overcome by using relative maximum boundary, therefore the application of the method for semi-guided learning is of great important.This paper studies the robustness of the convex risk minimization methods for fuzzy classification bases on optimization and functional analysis. The RMM fuzzy one-class classification methods are considered by using relative maximum boundary, the method of classification machine is obtained. The main contents are divided into the following three parts:In the first part, basic models and algorithms of SVM and fuzzy one-class support vector machine are analyzed on the framework of statistical learning theory. Combined with theory of the structural risk minimization, performance affected by the choice of different penalty parameter and kernel parameter in SVM classification is analyzed.In the second part, in terms of convex regularization risk minimization methods with twice continuously differentiable loss function, investigate robustness properties for such fuzzy learning methods. Firstly, we estimate robustness properties of learning algorithm by using the influence function. Next, by computing Gateaux derivate of the minimization functional and using Fredholm Alternative theorem, we give the upper bounds of the influence function under the appropriate conditions.In the third part, the paper introduces the basic idea of RMM method for fuzzy Semi-supervised learning problems, the relationship between RMM learning machine and SVM is analyzed. Then in terms of linear two-classification problems, fuzzy RMM one-class classification machine is established for different two kind models. by using Lagrangian multiplier, constrained optimization problem which determine the weight vector of classified hyperplane is converted to unconstrained optimization problem. Finally, generalize the result to non-linear two-classification problems by using feature map.