Strongly agree or strongly disagree?: Rating features in Support Vector Machines

In linear classifiers, such as the Support Vector Machine (SVM), a score is associated with each feature and objects are assigned to classes based on the linear combination of the scores and the values of the features. Inspired by discrete psychometric scales, which measure the extent to which a factor is in agreement with a statement, we propose the Discrete Level Support Vector Machine (DILSVM) where the feature scores can only take on a discrete number of values, defined by the so-called feature rating levels. The DILSVM classifier benefits from interpretability and it has visual appeal, since it can be represented as a collection of Likert scales, one for each feature, where we rate the level of agreement with the positive class. To construct the DILSVM classifier, we propose a Mixed Integer Linear Programming approach, as well as a collection of strategies to reduce computational cost. Our numerical experiments show that the three-point and the five-point DILSVM classifiers have comparable accuracy to the SVM with a substantial gain in interpretability and visual appeal, but also in sparsity, thanks to the appropriate choice of the feature rating levels.