Topological machine learning for multivariate time series

ABSTRACT

We develop a method for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances between the persistence diagrams and using the $k$-nearest neighbours algorithm ($k$-NN) for supervised machine learning. Two methods (symmetry-breaking and anchor points) are also introduced to enable TDA to better analyze data with heterogeneous features that are sensitive to translation, rotation or choice of coordinates. We apply our methods to room occupancy detection based on 5 time-dependent variables (temperature, humidity, light, CO₂ and humidity ratio). Experimental results show that topological methods are effective in predicting room occupancy during a time window. We also apply our methods to an Activity Recognition dataset and obtained good results.

KEYWORDS:

• Topological data analysis
• machine learning
• artificial intelligence
• multivariate time series
• room occupancy

Acknowledgments

The authors wish to thank the referees most warmly for numerous suggestions that have improved the exposition of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.