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A modified Markov transition probability-based network constructing method and its application on nonlinear time series analysis

Under the view point of complex networks, a Markov chain can he described by a weight directed graph, in which the weight of different edges is labeled by the Markov transfer probabilities ofjumping from current state to the future states. The original quantile graph method is based on the Markov transition probability with equal number of existing data points strategy. It ignored the amplitude information during constructing the associate network. In this brief paper, a modified quantile graph constructing method based on the Markov transition probability with equal distances interval dividing strategy is proposed. Sensitivity analysis of two algorithms in characterizing nonlinear time series are carried out based on the same EEG database, i.e., comparison of these two algorithms with each other were discussed via being applied on real data classification analysis. It is suggested that these two methods can be chosen for the analysis of nonlinear time series with uniform distributions or non-uniform distributions, respectively.