Large Margin Filtering
Many signal processing problems are tackled by filtering the signal for subsequent feature classification or regression. Both steps are critical and need to be designed carefully to deal with the particular statistical characteristics of both signal and noise. Optimal design of the filter and the classifier are typically aborded in a separated way, thus leading to suboptimal classification schemes. This paper proposes an efficient methodology to learn an optimal signal filter and a support vector machine (SVM) classifier jointly. In particular, we derive algorithms to solve the optimization problem, prove its theoretical convergence, and discuss different filter regularizers for automated scaling and selection of the feature channels. The latter gives rise to different formulations with the appealing properties of sparseness and noise-robustness. We illustrate the performance of the method in several problems. First, linear and nonlinear toy classification examples, under the presence of both Gaussian and convolutional noise, show the robustness of the proposed methods. The approach is then evaluated on two challenging real life datasets: BCI time series classification and multispectral image segmentation. In all the examples, large margin filtering shows competitive classification performances while offering the advantage of interpretability of the filtered channels retrieved.