A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Székely and Rizzo (2013). Specifically, a dissimilarity matrix formed the statistic to measure separation between finite-dimensional distributions component series. Once pairwise calculated, hierarchical method then applied obtain dendrogram. This procedure completely nonparametric as d...

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 ana...