Fitting B-spline curves by least squares support vector machines

The problem of construction of B-spline curves by a set of given points is an important issue in computer aided geometric design (CAGD). It is actually regression problem. The traditional way is least squares fitting of the data based on minimizing the empirical risk. Least squares support vector machines (LS-SVMs) are very effective methods for regression issue. How to use LS-SVMs to solve the problem of construction B-spline curve in reverse engineering is discussed in this paper. Whereas LS-SVMs are not suitable for the regression curves by B-spline form, a modified least squares support vector machines algorithm is proposed which operates on the principle of structure risk minimization instead of the empirical risk minimization; hence a better generalization ability is guaranteed. A new kernel function is used to make curves have the B-spline form. Our new method provides a new fitting way for CAGD. Through the examples, the robust is compared among different methods. Results demonstrate the validity of this new algorithm