Unsupervised Space-Time Clustering using Persistent Homology
Umar Islambekov, Mathematical Sciences, University of Texas at Dallas, USA
We present a new clustering algorithm for space-time data using the method of persistent homology. This method, having its roots in algebraic topology, is a popular tool in topological data analysis and it is used to extract topological information from data. A notable aspect of persistent homology 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.