Multi-resolution signal decomposition and approximation based on support vector machines

Both support vector machines (SVMs) and multi-resolution analysis (MRA) have been developed for solving signal approximation problem. When the scale function of MRA is adopted to act as the map function of SVMs, the high dimensional feature space in SVMs and the scale subspace in MRA will be the same Reproducing Kernel Hilbert Spaces (RKHS). Based on the fact, this paper proposes an algorithm for multi-resolution signal decomposition and approximation by employing approximation criterion of SVMs. The algorithm reduce the approximation error by introducing structure risk and have better smoothness property for approximation function. Experiments illustrate that our method has better approximation performance than conventional MRA when be applied it to stationary and non-stationary signals.