Topological Machine Learning for Multivariate Time Series

TL;DR

This paper introduces a topological data analysis framework for multivariate time series, converting data into point clouds and using Wasserstein distances with k-NN for classification, demonstrating effectiveness in occupancy detection and activity recognition.

Contribution

The paper presents novel TDA-based methods with symmetry-breaking and anchor points to improve analysis of heterogeneous multivariate time series.

Findings

Effective occupancy detection from multivariate data

Successful application to activity recognition datasets

Topological methods outperform some traditional approaches

Abstract

We develop a framework 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 neighbors 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.