To alleviate the attribute independence assumption, this paper proposes an auto-encoding naive Bayesian classifier (AE-NBC) which is trained based on transformed independent condition-attributes using an auto-encoding strategy. First, an auto-encoding neural network (AENN) with single hidden-layer is created to map the original data set to a high-dimensional data space. To guarantee the independence among auto-encoding condition-attributes (AECAs), an efficient and convergent objective function is elaborated to optimize the input-layer and output-layer weights of the AENN by considering both the auto-encoding error and attribute independence degree. Second, independent component analysis is iteratively carried out to remove the redundant attributes in AECAs so that the optimal transformed condition-attributes (TCAs) are obtained for the training of the NBC. Experiments were conducted on 29 benchmark data sets to validate the rationality, feasibility, and effectiveness of AE- NBC. Experimental results show that the independence among TCAs is stronger than among the original condition-attributes, and that AE- NBC can obtain higher training and testing accuracies than six Bayesian classifiers.

This paper proposes a compressed hidden naive Bayesian (C-HNB) classifier which is an improved version of hidden naive Bayesian (HNB) by compressing the Bayesian network structure and calculating the attribute correlation with maximal information coefficient (MIC). In C-HNB, we remodel the Bayesian network structure based on the chain rule of joint probability distribution so that the number of hidden parent nodes in C-HNB is smaller than the number of hidden parent nodes in HNB, which reduces the training complexity of Bayesian network. In addition, the attribute correlation in C-HNB is calculated with MIC rather than the mutual information, which makes the Bayesian network more stable because the calculation of mutual information is severely influenced by the discretization of continuous attribute. On the selected KEEL benchmark data sets, we compare the classification performances of C-HNB with HNB. The comparative results show that C-HNB can obtain the better prediction accuracy with the less training time in comparison with HNB and thus the experimental results demonstrate the effectiveness of C-HNB.