Pattern Identification Using Reconstructed Phase Space and Hidden Markov Model

In this paper we present a method for identification of temporal patterns that are predictive of events in a dynamic data system. The proposed new MRPS-HMM method applies a hybrid model using Reconstructed Phase Space (RPS) and stochastic state estimation via Hidden Markov Model (HMM) to search predictive patterns. This method constructs a multivariate phase space by embedding each data sequence with estimated time-delay and dimension. Multivariate sequences are categorized into three states: normal, patterns and events which are estimated by HMM. A penalized exponential loss function is used to estimates the optimal weights of each module of the classifier. We performed two experimental applications including a chaotic Rossler Map series and sludge volume bulking forecasting problem. Experiments results show that the new method significantly outperforms baseline methods.