In recent years there has been growing interest in applying techniques that incorporate knowledge from unlabeled data into systems performing supervised learning. The main motivation for this is the belief that classification performance can be improved by utilizing the contextual information provided by unlabeled data. This paper approaches the problem from a generative classifier perspective, and proposes a new kernel-based method based on combining likelihoods from the labeled examples with those of unlabeled examples. Preliminary results on synthetic low-dimensional data show that the performance of the technique is comparable to that of existing semi-supervised generative approaches based on mixture models trained using Expectation-Maximization. However, a distinct advantage of the proposed approach is that it relies on optimizing only a single parameter. The paper describes how this can be done using cross-validation.