On tuning a mean-field model for semi-supervised classification

Semi-supervised learning (SSL) has become an interesting research area due to its capacity for learning in scenarios where both labeled and unlabeled data are available. In this work, we focus on the task of transduction - when the objective is to label all data presented to the learner - with a mean-field approximation to the Potts model. Aiming at this particular task we study how classification results depend on $\beta$ and find that the optimal phase depends highly on the amount of labeled data available. In the same study, we also observe that more stable classifications regarding small fluctuations in $\beta$ are related to configurations of high probability and propose a tuning approach based on such observation. This method relies on a novel parameter $\gamma$ and we then evaluate two different values of the said quantity in comparison with classical methods in the field. This evaluation is conducted by changing the amount of labeled data available and the number of nearest neighbors in the similarity graph. Empirical results show that the tuning method is effective and allows NMF to outperform other approaches in datasets with fewer classes. In addition, one of the chosen values for $\gamma$ also leads to results that are more resilient to changes in the number of neighbors, which might be of interest to practitioners in the field of SSL.