LUMAWIG: Un-bottling the bottleneck distance for zero dimensional persistence diagrams at scale

Paul Samuel Ignacio, Jay-Anne Bulauan, David Uminsky

Keywords: Bottleneck distance, persistence diagrams, topological data analysis

TL;DR: A novel efficient algorithm for dimension zero bottleneck distance computation in topological data analysis.

Abstract: We present LUMÁWIG, a novel efficient algorithm to compute dimension zero bottleneck distance between two persistence diagrams of a specific kind which outperforms all other publicly available algorithm in runtime and accuracy. We bypass the overwhelming matching problem in previous implementations of the bottleneck distance, and prove that the zero dimensional bottleneck distance can be recovered from a very small number of matching cases. LUMÁWIG also generally enjoys linear complexity as shown by empirical tests. This allows us to scaleTDA to data sets of sizes encountered in machine learning and utilize persistence diagrams in a manner that goes beyond the simple use of the most persistent components.

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