A parameter selection method of the deterministic anti-annealing algorithm for network exploring

The traditional expectation maximization (EM) algorithm for the mixture model can explore the structural regularities of a network efficiently. But it always traps into local maxima. A deterministic annealing EM (DAEM) algorithm is put forward to solve this problem. However, it brings about the problem of convergence speed. A deterministic anti-annealing expectation maximization (DAAEM) algorithm not only prevents poor local optima, but also improves the convergence speed. Thus, the DAAEM algorithm is used to estimate parameters of the mixture model. This algorithm always sets its initial parameter β0 by experience, which maybe get trapped into meaningless results due to too small β0, or converge to local maxima more frequently due to too large β0. A parameter selection method for β0 is designed. In our method, the convergence rate of the DAAEM algorithm for mixture model is first derived from Jacobian matrix of the posterior probabilities. Then the theoretical lower bound of β0 is computed based on the convergence rate at meaningless points. In our experiments we select β0 by rounding up the lower bound to the nearest tenth. Experiments on real and synthetic networks demonstrate that the parameter selection method is valid, and the performance of the DAAEM algorithm beginning from the selected parameter is better than the EM and DAEM algorithms for mixture model. In addition, we find that the convergence rate of the DAAEM algorithm is affected by assortative mixing by degree of a network.