Motif Extraction using an Improved Iterative Duplication Method for HMM Topology Learning

In this paper, Hidden Markov Models (HMMs) are utilized to represent motifs. Motifs are the preserved sites in the evolution process and are considered to represent the function or structure of proteins. It is compulsory to use direct periodic topology and the OR rule to represent motifs. The direct periodic topology is necessary to represent cyclic structures, such as global loops for helices. The OR rule is necessary to represent di erent families or types in motifs. Therefore, to represent motifs, HMMs must contain direct periodic topology and OR rule. In order to obtain an optimal HMM topology for a motif, we improved the \iterative duplication method"[1]. In this method, a small fully-connected HMM is gradually expanded by a state splitting. The initial number of the states is set to three in the current implementation. It iterates through a parameter estimation phase followed by a topology modi cation phase. It terminates when the accuracy of model size selection data is maximum. For parameter estimation, the Baum-Welch algorithm is used on several initial HMMs with randomized parameters to avoid converging in the local maximum. Then, the best HMM is chosen based on the likelihood of training data. In the topology modi cation phase, negligible transition deletion, negligible state deletion, splitting state selection and state splitting is performed. The negligible transition deletion is performed by deleting the transitions with negligible transitional probability, the threshold is = max( 1 ; r), where 1 is a smoothing value and r is a convergence radius. The purpose of deleting the transitions is to keep the topology space small and consequently to reduce the computation for the parameter estimation. The negligible state deletion is performed by deleting states with negligible initial probabilities and negligible incoming transitions. This state deletion also reduces the training computation and has a good e ect for calculating the criteria of splitting state. The