Geometry Helps to Compare Persistence Diagrams
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1226492
- Report Number(s):
- LBNL-1003849; ir:1003849
- Resource Relation:
- Conference: ALENEX16. Meeting on Algorithm Engineering and Experiments, Arlington, VA (United States), 10-12 Jan 2016
- Country of Publication:
- United States
- Language:
- English
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