The fusion of wavelet technique and support vector machines (SVMs) has become an intensive study in recent years. Considering that the wavelet technique is the theoretical foundation of multiresolution analysis (MRA), it is valuable for us to investigate the problem of whether a good performance could be obtained if we combine the MRA with SVMs for signal approximation. Based on the fact that the feature space of SVM and the scale subspace in MRA can be viewed as the same Reproducing Kernel Hilbert Spaces (RKHS), a new algorithm named multiresolution signal decomposition and approximation based on SVM is proposed. The proposed algorithm which approximates the signals hierarchically at different resolutions, possesses better approximation of smoothness for signal than conventional MRA due to using the approximation criterion of the SVM. Experiments illustrate that our algorithm has better approximation of performance than the MRA when being applied to stationary and non-stationary signals.
On Stochastic Optimization and Statistical Learning in Reproducing Kernel Hilbert Spaces by Support Vector Machines (SVM)
