Quantum clustering-based weighted linear programming support vector regression for multivariable nonlinear problem

Linear programming support vector regression shows improved reliability and generates sparse solution, compared with standard support vector regression. We present the v-linear programming support vector regression approach based on quantum clustering and weighted strategy to solve the multivariable nonlinear regression problem. First, the method applied quantum clustering to variable selection, introduced inertia weight, and took prediction precision of v-linear programming support vector regression as evaluation criteria, which effectively removed redundancy feature attributes and also reduced prediction error and support vectors. Second, it proposed a new weighted strategy due to each data point having different influence on regression model and determined the weighted parameter p in terms of distribution of training error, which greatly improved the generalization approximate ability. Experimental results demonstrated that the proposed algorithm enabled the mean squared error of test sets of Boston housing, Bodyfat, Santa dataset to, respectively, decrease by 23.18, 78.52, and 41.39%, and also made support vectors degrade rapidly, relative to the original v-linear programming support vector regression method. In contrast with other methods exhibited in the relevant literatures, the present algorithm achieved better generalization performance.