A Hybrid Markov Model Based on EM Algorithm

Abstract

Order-k Markov model can be used in many fields such as natural language understanding, coding, mobile path prediction and so on to make prediction and then control. But the model has to face the problem of state space expansion. Taking the mobile path prediction as the research background, the paper firstly proposes a step-k Markov model and validates its feasibility. Secondly, a hybrid Markov predictor model is put forward based on the step-k Markov model. The complexity of the hybrid Markov model is O(N) while the order-k Markov model is O(N2 ). And the memory demand of the hybrid Markov model is O(N2 ) while order-k Markov model is O(N3). Finally, it is proved that the hybrid Markov predictor can get close performance with order-k Markov predictor at much lower expense by conditional entropy analysis and user mobility data analysis. Also it can alleviate the zero probability problem in order-k Markov model to some extent. The hybrid Markov predictor is more practical than order-k Markov predictor under WLAN