Machine learning of time series data using persistent homology

This study proposes a novel method for time-series analysis based on persistent homology. Traditional time-series analysis techniques based on persistent homology often involve high computational costs. To address this challenge, we introduce the use of recurrence plots. In our approach, recurrence plots are first generated from the datasets, and topological information is then extracted from these plots using persistent homology. The obtained topological information are vectorized through persistence image and the resulting vectors are further reduced using non-negative matrix factorization. The features derived from this method encapsulate rich and distinctive information inherent in the dataset. We applied the proposed approach to several synthetic and experimental datasets to demonstrate its effectiveness. Our method successfully identified the periodic-to-chaotic and chaotic-to-chaotic transitions in Chua's system and revealed distinguishing characteristics in electromyograms from healthy, neuropathic, and myopathic individuals. Additionally, the extracted features enabled accurate classification of electrocardiogram data. Overall, the results indicate that the features obtained through this method capture essential information embedded in time-series data.