Semi-Supervised Nearest Mean Classification Through a Constrained Log-Likelihood

We cast a semi-supervised nearest mean classifier, previously introduced by the first author, in a more principled log-likelihood formulation that is subject to constraints. This, in turn, leads us to make the important suggestion to not only investigate error rates of semi-supervised learners but also consider the risk they originally aim to optimize. We demonstrate empirically that in terms of classification error, mixed results are obtained when comparing supervised to semi-supervised nearest mean classification, while in terms of log-likelihood on the test set, the semi-supervised method consistently outperforms its supervised counterpart. Comparisons to self-learning, a standard approach in semi-supervised learning, are included to further clarify the way, in which our constrained nearest mean classifier improves over regular, supervised nearest mean classification.