Comparison Research Of SVR Algorithms Based On Several Loss Functions

Support vector machine is formed by Vapnik in the early1990s. As a new learning machine, it is put forward based on the statistical learning theory and structural risk minimization principle. Because of its excellent learning ability, it can solve the small sample, nonlinear, high dimension problems, it has attracted increasing attention and more and more applications in pattern recognition, function estimation, prediction model in the domestic and foreign academic circles.Support vector machines with the help of loss function are used to solve the regression problems which called support vector regression (SVR). Gauss loss function, s-insensitive loss function, Huber loss function and Laplace loss function are the popular loss functions. The theory and practical application of SVR algorithm based on ε-insensitive loss function are relatively more mature than the other SVR algorithms, so the theory of SVR algorithms based on Gauss loss function, Huber loss function and Laplace loss function still needs further improvement.Firstly, this article describes the theory of SVR algorithm based on ε-insensitive loss function. Then according to Lagrange dual theory the other three kinds of loss function SVR algorithm are deduced from their original optimization problems. At last, through data analysis of exchange rate between China and USA, we compare SVR algorithms based on the four different loss functions with the advantages of SVR algorithm and Auto Regression (AR) model. Numerical experiment we focus on the SVR algorithm for selecting each parameter. The parameter selection method this paper used can be enlightened for the further study.Finally, this paper makes a summary about the four SVR algorithms based on different loss functions, and gives some further outlook about the data analysis and prospects to make improvement on loss function.