Optimal Transport Based Change Point Detection and Time Series Segment Clustering

TL;DR

This paper introduces a novel, distribution-free change point detection algorithm based on optimal transport, capable of offline and online analysis, and applies spectral clustering for time series segment grouping, demonstrating effectiveness on synthetic and real data.

Contribution

It presents a new Wasserstein-based change point detection method and a spectral clustering approach for segment grouping, advancing unsupervised time series analysis.

Findings

Effective in synthetic data tests

Demonstrates robustness on real datasets

Reduces false positives in change point detection

Abstract

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.