Unsupervised Space-Time Clustering using Persistent Homology
This provides a novel approach for researchers analyzing complex space-time datasets, such as environmental monitoring, though it appears incremental as it adapts existing topological tools to clustering.
The paper tackles the problem of clustering space-time data by developing a new algorithm based on persistent homology, which analyzes data at multiple resolutions to distinguish true features from noise. The algorithm is evaluated on synthetic data and applied to a water quality case study in the Chesapeake Bay, showing competitive performance compared to methods like K-means and DBSCAN.
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.