Possibilistic Classification Learning Based on Contrastive Loss in Learning Vector Quantizer Networks

Classification in a possibilistic scenario is a kind of multiple class assignments for data. One of the most prominent and interpretable classifier is the learning vector quantization (LVQ) realizing a nearest prototype classifier model. Figuring out the problem of classifying based on possibilistic or probabilistic class labels (assignments) leads to the use of likelihood ratio to organize a sustainable approach. To this end, we start with a special kind of probabilistic LVQ, known as Robust Soft LVQ, and propose a possibilistic extension to pave the way to our new method. Particularly, the proposed possibilistic variant takes positive and negative reasoning known from RSLVQ into account to secure a contrastive learning model in the end. In the paper we will explain the model and give the mathematical justification.