The Research Of SVM Classifier Method Based On Gilbert Algorithm And Scaled Convex Hulls

In recent years, support vector machine(short name SVM) which is based on statistical learning theory has become a hot research topic in the field of machine learning. Traditional machine learning methods are based on the empirical risk minimization principle,but support vector machine is based on structural risk minimization theory. SVM has many advantages, global optimization and good adaptability,but it also has some disadvantages, the computing cost of training algorithm is huge, the efficiency is not high when dealing with large-scale samples. When the data samples are non-linear separable, some sample misclassification situation exist,there are more complex calculation in the process of SVM training.The accuracy and training speed of SVM classification model are affected. In this paper, we do depth research in these issues, the main research work are as follows:(1) Non-linear separable problem can be handled by soft margin SVM,which is adding a slack variable to the constraint to transform non-linear separable problem into a more simple problem, but slack variable is difficult to choose. Literature [1] introduced scaled convex hull ideology, selected a compression ratio of the two convex hulls and compressed them until the two samples can be divided, but the method of determining whether two convex hulls is separable was not accurate enough and the choose of the compression ratio value was blind. To solve these problems, this paper presents a new method to judge whether the scaled convex hulls are separable,the new method calculate the cross-depth of the data samples which can be used to estimate the range of compression ratio. We can determine the compression ratio candidate value set, so that the value of the compression ratio is no longer blind to choose, in this way,we can quickly calculate the compression ratio This method can accurately determine whether the convex hull can be divided into two, to avoid unnecessary compression, the compression ratio is also more accurate, which directly affects the performance of the classifier(2)Gilbert algorithm is a solution of quadratic programming, due to its small amount of computation for each iteration, it can be used as a training algorithm of support vector machine to handle large-scale data problems. This paper focuses on the main disadvantage of Gilbert method, its slow convergence, the convergence rate is affected by three factors:the initial point selection, updating strategy, judgement of convergence condition.(3) Gilbert algorithm is used to find the nearest point between geometric convex hulls.The biggest drawback of Gilbert algorithm is that in many cases, as it approaches the optimum solution the convergence speed is very slow. When the iteration point is more closer to the optimal solution in the process of iteration, it will hover around the optimal solution, it is difficult to reach the optimal solution. This paper propose a new iterative strategy based on Gilbert algorithm.In this way,the new algorithm can reduce the number of iterations and accelerate the convergence speed. Experiment results show that the improved algorithm accelerates the speed of solution and convergence speed.(4) Combining with the improved Gilbert algorithm and scaled convex hull theory, we design a new support vector machine classifier,and select a number of data sets from the international standard UCI data sets to do comparative experiments with the existing similar algorithms, the experiment results show that the proposed algorithm increases the training speed in the condition of ensuring the accuracy of data classification.