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Decomposition hybrid algorithms with the recursive framework which recursively decompose the structural task into structural subtasks to reduce computational complexity are employed to learn Bayesian network (BN) structure. Merging rules are commonly adopted as the combination method in the combination step. The direction determination rule of merging rules has problems in using the idea of keeping v-structures unchanged before and after combination to determine directions of edges in the whole structure. It breaks down in one case due to appearances of wrong v-structures, and is hard to operate in practice. Therefore, we adopt a novel approach for direction determination and propose a two-stage combination method. In the first-stage combination method, we determine nodes, links of edges by merging rules and adopt the idea of permutation and combination to determine directions of contradictory edges. In the second-stage combination method, we restrict edges between nodes that do not satisfy the decomposition property and their parent nodes by determining the target domain according to the decomposition property. Simulation experiments on four networks show that the proposed algorithm can obtain BN structure with higher accuracy compared with other algorithms. Finally, the proposed algorithm is applied to the thickening process of gold hydrometallurgy to solve the practical problem.

A decomposition structure learning algorithm in Bayesian network based on a two-stage combination method