Discussion On Support Vector Machine

Statistical learning theory (SLT) is a general theory related to the machine learning using empirical data. It systematically considers the situation that the number of samples is limited, so its practicality is better than the traditional statistical theory. The support vector machine (SVM), which is developed on the basic of SLT, is widely recognized because of its better promotion ability in the case of limited samples. It is different from the other machine learning algorithms (They only use empirical risk minimization principle). It uses the structural risk minimization principles to train the learning machine, and applies VC-dimensional theories to measure the structure risk. SVM is a master of a number of standard techniques within the field of machine learning. It not only integrates the largest interval hyper-plane and convex quadratic programming techniques, but also integrates Mercer nuclear, slack variables, sparse solution techniques and so on. And it has the best performance in many challenging applications (such as pattern recognition, regression estimation, etc.).This paper introduces, firstly, the machine learning and statistical learning theory, and describes the characteristics of support vector machines on this basis. This thesis involves two aspects mainly:Firstly, the expression of new smooth functions of SVM and its performance analysis. The results shows that:the approximation performance of new smooth function is better than that of the lower order smooth function, thus, it prepares a new smooth function for the further study on SVM. Secondly, the probability density estimation based on multi-core and structure adjustable SVM. This article combines the P method (which is specifically address the not fixed problem) and multi-core structure adjustable SVM to solve the problem of probability density estimation. The method we propose can be used widely because it has more robust than that of the standard SVM.