Localized generalization error of Gaussian-based classifiers and visualization of decision boundaries

In pattern classification problem, one trains a classifier to recognize future unseen samples using a training dataset. Practically, one should not expect the trained classifier could correctly recognize samples dissimilar to the training dataset. Therefore, finding the generalization capability of a classifier for those unseen samples may not help in improving the classifiers accuracy. The localized generalization error model was proposed to bound above the generalization mean square error for those unseen samples similar to the training dataset only. This error model is derived based on the stochastic sensitivity measure(ST-SM)of the classifiers. We present the ST-SMS for various Gaussian based classifiers: radial basis function neural networks and support vector machine in this paper. At the end of this work, we compare the decision boundaries visualization using the training samples yielding the largest sensitivity measures and the one using support vectors in the input space.