MRA Kernel Matching Pursuit Machine

Kernel Matching Pursuit Machine (KMPM) is a relatively new learning algorithm utilizing Mercer kernels to produce non-linear version of conventional supervised and unsupervised learning algorithm. But the commonly used Mercer kernels can’t expand a set of complete bases in the feature space (subspace of the square and integrable space). Hence the decision-function found by the machine can’t approximate arbitrary objective function in feature space as precise as possible. Multiresolution analysis (MRA) shows promise for both nonstationary signal approximation and pattern recognition, so we combine KMPM with multiresolution analysis technique to improve the performance of the machine, and put forward a MRA shift-invariant kernel, which is a Mercer admissive kernel by theoretical analysis. An MRA kernel matching pursuit machine (MKMPM) is constructed in this paper by Shannon MRA shift-invariant kernel. It is shown that MKMPM is much more effective in the problems of regression and pattern recognition by a large number of comparable experiments.