Abstract: Although the traditional expectation-maximization (EM) algorithm of the mixed model can effectively explore the structural regularity of the network, it always gets stuck in some local maximum. A deterministic annealing expectation maximization (NMEM) algorithm is proposed to solve this problem, which not only prevents local optimum but also improves convergence speed and is thus used to estimate the parameters of the hybrid model. The algorithm always sets its initial parameters β0 through experience. If β0 is too small, the results are meaningless, or if β0 is too large, it will converge to the local maximum more frequently. Furthermore, a new hybrid model of directional network and a parameter selection method of β0 were designed.

Key words: mixture model, annealing algorithm, convergence rate, directed network