Optimal Transport Based Change Point Detection And Time Series Segment Clustering

Two common problems in time series analysis are the decomposition of the data stream into disjoint segments, each of which is in some sense “homogeneous” - a problem that is also referred to as Change Point Detection (CPD) - and the grouping of similar nonadjacent segments, or Time Series Segment Clustering (TSSC). Building upon recent theoretical advances characterizing the limiting distribution free behavior of the Wasserstein two-sample test, we propose a novel algorithm for unsupervised, distribution-free CPD, which is amenable to both offline and online settings. We also introduce a method to mitigate false positives in CPD, and address TSSC by using the Wasserstein distance between the detected segments to build an affinity matrix to which we apply spectral clustering. Results on both synthetic and real data sets show the benefits of the approach.