Topological Time-series Classification

Abstract

We establish a strong connection between Topological Data Analysis (TDA)and the field of time-series classification. This is accomplished via two novel contri- butions. The first is a method for extracting topological information from a time series in a manner which circumvents the expensive computation normally required. The second is an adaption of an existing topological summary to create an efficient topological time-series pooling operator. Taken together, these insights enable a new classifier, TopRocket (Topological Random Convolutional Kernel Transform). Using standard comparison methods, TopRocket ranks second among all univariate time-series classifiers. Further, TopRocket is the best performing scalable classifier. As a final contribution, we provide the fastest available implementation of the algo- rithm for computing time-series sublevel set persistence. This provides a foundation for further investigation of TDA for time-series classification. This work lies at the intersection of TDA and machine learning, where suc- cess is dependent on efficiently extracting topological information from data and using that information with downstream models. For this purpose, we develop an efficient, data-based, topological summary, the Betti pooling operator. We rigor- ously demonstrate the utility of TopRocket by evaluating its performance against the University of California Riverside (UCR) Time Series Archive, a widely used benchmark collection of data sets. TopRocket is the first TDA-based classifier to obtain state-of-the art results on any similarly competitive problem. We strongly believe that TDA will play a central role in the future of machine learning.