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.

摘要

我们开发了一种使用拓扑数据分析（TDA）方法分析多元时间序列的方法。拟议的方法包括将多元时间序列转换为点云数据，计算余辉图之间的Wasserstein距离并使用$ķ$近邻算法（$ķ$-NN）进行有监督的机器学习。还引入了两种方法（对称断开和锚点），以使TDA能够更好地分析具有对平移，旋转或坐标选择敏感的异构特征的数据。我们基于5个时间相关变量（温度，湿度，光线，CO ₂和湿度比）将我们的方法应用于房间占用检测。实验结果表明，拓扑方法可以有效地预测一个时间窗口内的房间占用情况。我们还将我们的方法应用于活动识别数据集并获得了良好的结果。