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

The paper introduces Atlas for Recurrence neighborhood (ARN) Model– a novel topological method for prediction and modeling for a nonlinear time-series that exhibits recurring patterns. According to the model, global manifold of a reconstructed state-space can be approximated by a few overlapping recurrence neighborhoods. The inherent redundancy structure of the delayembedding procedure and the property of recurrence are used to reduce the computational load, which is inevitable in nonlinear analysis. The modeling and prediction capabilities of the model are demonstrated using (i) a numerical data generated by a dynamical system: the Duffing oscillator and (ii) a real-world data: an Electrocardiogram ECG recording of a healthy human. A potential application of the proposed model is demonstrated for a multivariate cardiovascular data set that exhibit recurring patterns. 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 of brain such as predicting loss of data or identifying noises in the physiological data. Potentials of the proposed ARN model to perform a cognitive task–‘the prediction of gaps or loss of data based on the contextual information’ are explored in the study reported here, analysing a set of 100 multichannel cardiovascular recordings. One Sentence Summary: A topological model for prediction and modeling for a time-series that exhibits recurring patterns.