Semi-supervised Bayesian classification by vector features with continuous and discrete components

A solution for the traditional Bayesian classification problem in non-traditional conditions is proposed, when the distributions and a priori probabilities of classes are unknown, but a trained sample from the zero class (labeled positive) and mixed sample (unlabeled) are available. Mixed sample will be employed in the learning to restore mixed distribution and as a test sample for constructed classifier. The case with vector features containing continuous and discrete components is considered. To restore unknown distributions nonparametric kernel techniques with data-driven bandwidth are used. A new algorithm for estimating the prior probability of zero class is given using positive labeled and unlabeled samples. This allows to find a good approximation of optimal threshold for the modified Bayesian classification algorithm. Numerical verification confirms the effectiveness of the proposed classification technique even in cases of strong overlapping of class distributions.