  This paper presents a new clustering algorithm for space-time data based on
the concepts of topological data analysis and in particular, persistent
homology. Employing persistent homology - a flexible mathematical tool from
algebraic topology used to extract topological information from data - in
unsupervised learning is an uncommon and a novel approach. A notable aspect of
this methodology consists in analyzing data at multiple resolutions which
allows to distinguish true features from noise based on the extent of their
persistence. We evaluate the performance of our algorithm on synthetic data and
compare it to other well-known clustering algorithms such as K-means,
hierarchical clustering and DBSCAN. We illustrate its application in the
context of a case study of water quality in the Chesapeake Bay.
