Non-linear modeling of variables relationship in multiple time-series data with extended dynamic interaction network

The challenge of being able to learn and model hidden behavior in time-series data has been investigated extensively in the studies of dynamic systems. Nevertheless, these previous researches have emphasized more on the task to model movement of a solitary time-series in order to forecast their future values and rarely gave interest to further learn about their governing behavior. Therefore, we have previously introduced an adaptive machine learning method, named the Dynamic Interaction Network (DIN) model, to discover and represent dynamic patterns of interaction from multiple time-series data. However, the interactions were modeled only as linear structures which are abridged representations of compound relationships between series collected from real world settings. Consequently, this research aims in extending the previously developed method to enable the modeling of non-linear relationship between collections of variables in multiple time-series data. The objective is realized by incorporating the extended Kalman filter method into the DIN model. Comparative study and results of conducted experiments reveals that the ability to model the dynamic interaction between variables in non-linear forms leads to better understanding of the nature of observed system and in addition helps to increase the prediction accuracy.