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| Title | A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams |
| Authors | Rolando Kindelan, Mircea Petrache, Mauricio Cerda, Nancy Hitschfeld |
| Publication date | 2024 |
| Abstract | Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics which are accurate, theoretically sound, and fast to compute. Especially for denser multi-dimensional PDs, such compari- son metrics are lacking. While on the one hand, Wasserstein- type distances have high accuracy and theoretical guarantees, they incur high computational cost. On the other hand, dis- tances between vectorizations such as Persistence Statistics (PS)s have lower computational cost, but lack the accuracy guarantees and in general they are not guaranteed to dis- tinguish PDs (i.e. the two PS vectors of different PDs may be equal). In this work we introduce a class of pseudodis- tances called Extended Topological Pseudodistances (ETD)s, which have tunable complexity, and can approximate Sliced and classical Wasserstein distances at the high-complexity extreme, while being computationally lighter and close to Persistence Statistics at the lower complexity extreme, and thus allow users to interpolate between the two metrics. We build theoretical comparisons to show how to fit our new dis- tances at an intermediate level between persistence vector- izations and Wasserstein distances. We also experimentally verify that ETDs outperform PSs in terms of accuracy and outperform Wasserstein and Sliced |
| Pages | 13202-13210 |
| Conference name | Annual AAAI Conference on Artificial Intelligence |
| Publisher | Association for the Advancement of Artificial Intelligence (www.aaai.org) |
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