ABSTRACT
Persistent homology, one of themost important theories in algebraic
topology, has attracted much attention in a growing number of
studies such as clustering, shape analysis, natural image statistics
and object recognition, showing its great potential in the tasks
of pattern recognition. However, persistent homology is defined
based on the knowledge of both the group theory and topology,
which is not popular in the community of pattern recognition
and not easy to get access for non-specialists. In this chapter, we
make such a timely survey for pattern recognition, in which (1)
mathematical backgrounds are extensively described; (2) various
applications with persistent homology are introduced; (3) their
relations are exploited and concluded as an appropriate taxonomy;
(4) and finally open directions are discussed. It is believed that
this work will benefit both beginners and practitioners in the area
of pattern recognition, and thus promote the future development
of this field.
