Validation of the combination algorithm.

Where is the number of variables in the database, is the number of samples in the database, similarity is the average proportion of the number of identical edges between and to the total number of edges in and , and is the execution time of the Bayesian network combination program. The table shows that the similarity is depend on the number of samples, this is because the algorithms are based on the computation of probabilities and the accuracy of computation of probability is sensitive to the number of samples. Specifically, there are two reasons: (a)The real distributions of variables can't be reflected if the database only have several samples; (b)The equation we used to compute the probabilities is sensitive to the number of samples. Then in the experiments on and , similarity , this is because the two databases have enough samples and can provide enough information for constructing the real Bayesian networks, then the learned Bayesian networks , and are completely the same. So, consensus Bayesian network , and and are the same. Similarity and execution time are the results of the experiments using the fusion method proposed by Zhang et al. [19] instead of our combination algorithm. and show that our algorithm works more efficiently. The time complexity of our algorithm is , where is the number of nodes in the network. However, the execution time of Zhang's fusion method grows exponentially as the size of the biggest clique in the Clique tree increases.