Rescale-invariant SVM for binary classification

Support Vector Machines (SVM) are among the best-known machine learning methods, with broad use in different scientific areas. However, one necessary pre-processing phase for SVM is normalization (scaling) of features, since SVM is not invariant to the scales of the features' spaces, i.e., different ways of scaling may lead to different results. We define a more robust decision-making approach for binary classification, in which one sample strongly belongs to a class if it belongs to that class for all possible rescalings of features. We derive a way of characterising the approach for binary SVM that allows determining when an instance strongly belongs to a class and when the classification is invariant to rescaling. The characterisation leads to a computational method to determine whether one sample is strongly positive, strongly negative or neither. Our experimental results back up the intuition that being strongly positive suggests stronger confidence that an instance really is positive.