Constrained parameter estimation for semi-supervised learning: The case of the nearest mean classifier

Abstract

A rather simple semi-supervised version of the equally simple nearest mean classifier is presented. However simple, the proposed approach is of practical interest as the nearest mean classifier remains a relevant tool in biomedical applications or other areas dealing with relatively high-dimensional feature spaces or small sample sizes. More importantly, the performance of our semi-supervised nearest mean classifier is typically expected to improve over that of its standard supervised counterpart and typically does not deteriorate with increasing numbers of unlabeled data. This behavior is achieved by constraining the parameters that are estimated to comply with relevant information in the unlabeled data, which leads, in expectation, to a more rapid convergence to the large-sample solution because the variance of the estimate is reduced. In a sense, our proposal demonstrates that it may be possible to properly train a known classification scheme such that it can benefit from unlabeled data, while avoiding the additional assumptions typically made in semi-supervised learning. © 2010 Springer-Verlag Berlin Heidelberg.