Fixed-size least squares support vector machines: a large scale application in electrical load forecasting

Based on the Nystrom approximation and the primal-dual formulation of the least squares support vector machines, it becomes possible to apply a nonlinear model to a large scale regression problem. This is done by using a sparse approximation of the nonlinear mapping induced by the kernel matrix, with an active selection of support vectors based on quadratic Renyi entropy criteria. The methodology is applied to the case of load forecasting as an example of a real-life large scale problem in industry. The forecasting performance, over ten different load series, shows satisfactory results when the sparse representation is built with less than 3% of the available sample.