  The problem of rapid and automated detection of distinct market regimes is a
topic of great interest to financial mathematicians and practitioners alike. In
this paper, we outline an unsupervised learning algorithm for clustering
financial time-series into a suitable number of temporal segments (market
regimes). As a special case of the above, we develop a robust algorithm that
automates the process of classifying market regimes. The method is robust in
the sense that it does not depend on modelling assumptions of the underlying
time series as our experiments with real datasets show. This method -- dubbed
the Wasserstein $k$-means algorithm -- frames such a problem as one on the
space of probability measures with finite $p^\text{th}$ moment, in terms of the
$p$-Wasserstein distance between (empirical) distributions. We compare our
WK-means approach with a more traditional clustering algorithms by studying the
so-called maximum mean discrepancy scores between, and within clusters. In both
cases it is shown that the WK-means algorithm vastly outperforms all considered
competitor approaches. We demonstrate the performance of all approaches both in
a controlled environment on synthetic data, and on real data.
