A novel Topological Model for Nonlinear Analysis and Prediction for Observations with Recurring Patterns

Abstract

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few overlapping recurrence neighborhoods. The inherent redundancy structure of the delay embedding procedure and the property of recurrence are used to reduce the computational load, which is inevitable in nonlinear analysis. The modeling and prediction possibilities of the model are demonstrated using (i) a numerical data generated by a dynamical system: the Duffing oscillator and (ii) a real--life data: Electrocardiogram ECG data of a healthy human. A potential application of the proposed model is demonstrated for a multivariate cardiovascular data set that exhibits the property of recurrence. Real--time monitoring of cardiovascular signals are essential in clinical research and corruption of data are very common. It is a challenging task for a model to perform cognitive functions based on the contextual information, explicitly predicting gaps or loss of data and identifying noises in the physiological data. Paper concludes with an application of the proposed model in addressing some of these the issues.