Householder transformation based sparse least squares support vector regression

Sparseness is a key problem in modeling problems. To sparsify the solution of normal least squares support vector regression (LSSVR), a novel sparse method is proposed in this paper, which recruits support vectors sequentially by virtue of Householder transformation, here HSLSSVR for short. In HSLSSVR, there are two benefits. On one hand, a recursive strategy is adopted to solve the linear equation set instead of solving it from scratch. During each iteration, the training sample incurring the maximum reduction on the residuals is recruited as support vector. On the other hand, in the process of solving the linear equation set, its condition number does not deteriorate, so the numerical stability is guaranteed. The reports from experiments on benchmark data sets and a real-world mechanical system to calculate the inverse dynamics of a robot arm demonstrate the effectiveness and feasibility of the proposed HSLSSVR.