Morse theory in topological data analysis
Henry Adams, Atanas Atanasov, Gunnar Carlsson · arXiv (Cornell University) · 2011
Abstract. We introduce a method for analyzing high-dimensional data. Our approach is inspired by Morse theory and uses the nudged elastic band method from computational chemistry. As output, we produce an increasing sequence of cell complexes modeling the dense regions of the data. We test the method on several data sets and obtain small cell complexes revealing informative topological structure.