Probabilistic extension and reject options for pairwise LVQ

Learning vector quantization (LVQ) enjoys a great popularity as efficient and intuitive classification scheme, accompanied by a strong mathematical substantiation of its learning dynamics and generalization ability. However, popular deterministic LVQ variants do not allow an immediate probabilistic interpretation of its output and an according reject option in case of insecure classifications. In this contribution, we investigate how to extend and integrate pairwise LVQ schemes to an overall probabilistic output, and we compare the benefits and drawbacks of this proposal to a recent heuristic surrogate measure for the security of the classification, which is directly based on the LVQ classification scheme. Experimental results indicate that an explicit probabilistic treatment often yields superior results as compared to a standard deterministic LVQ method, but metric learning is able to annul this difference.