  Two common problems in time series analysis are the decomposition of the data
stream into disjoint segments that are each in some sense "homogeneous" - a
problem known as Change Point Detection (CPD) - and the grouping of similar
nonadjacent segments, a problem that we call Time Series Segment Clustering
(TSSC). Building upon recent theoretical advances characterizing the limiting
distribution-free behavior of the Wasserstein two-sample test (Ramdas et al.
2015), 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.
