A New Weighted Support Vector Regression and its Application in Ship's Principal Characteristics Mathematical Modeling

摘要

Mathematical modeling on ship's principal characteristics is a very important and useful task. The Support Vector Machines (SVM), a new general machine learning method based on the frame of statistical learning theory, is an effective method of processing the non-liner classification and regression. Because of its solid theoretical background and excellent generalization performance, it has become the hotspot of machine learning. This method can solve those practical problems such as limited samples, high dimension, non-linear problem and local minimum. Recently, Support Vector Regression (SVR) has been introduced to solve regression and prediction problems and widely used in many fields. With the analysis of both advantages and disadvantages of current support vector regression based on Gaussian kernel function, we propose a new weighted support vector regression algorithm in this article, thus the rigorous constraint is overcome that maintains "corresponding parameters of kernel function support vectors should be equal". In this proposed algorithm, a new kernel function is brought forward with weight factors: K(x_i,X_j)=exp(-(||x_i,X_j)~2)/(σ_i~2+σ_j~2) and the weight vector W = (w_i,w_2,...,w_n)~T is decided by the input vector X = (x_1,x_2,...,x_n)~T . And based on this new proposed SVR method, we apply it in the offshore support vessel's principal characteristics mathematical modeling in scientific research project, and compare the result with ordinary regression method and Neural Network method. The results of experiment show the practicability and effectiveness of this algorithm in the field of ship's principal characteristics mathematical modeling.