Topological machine learning for multivariate time series

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