We use the nudged elastic band method from computational chemistry to analyze high-dimensional data. Our approach is inspired by Morse theory, and as output we produce an increasing sequence of small cell complexes modeling the dense regions of the data. We test the method on data sets arising in social networks and in image processing. Furthermore, we apply the method to identify new topological structure in a data set of optical flow patches.
Bibliographical notePublisher Copyright:
© 2015 Juliusz Schauder Centre for Nonlinear Studies.
Copyright 2020 Elsevier B.V., All rights reserved.
- Morse theory
- Nudged elastic band
- Topological data analysis