The DOPE Distance is SIC: A Stable, Informative, and Computable Metric on Ordered Merge Trees

Author

Jose Arbelo, Ursinus CollegeFollow
Antonio Delgado, Ursinus CollegeFollow
Charley Kirk, Juniata CollegeFollow
Zach Schlamowitz, University of ArizonaFollow

Submission Date

7-30-2022

Document Type

Paper

Department

Mathematics

Second Department

Computer Science

Faculty Mentor

Christopher Tralie

Second Faculty Mentor

Nicholas Scoville

Comments

Presented during the 24th Annual Summer Fellows Symposium, July 22, 2022 at Ursinus College.

This research was supported by The National Science Foundation and The Andrews Family Fellows Fund.

Presented also at The MAA Undergraduate Student Poster Session 2022.

The downloadable ZIP file contains background information, examples of merge trees and the new metric, and an animation of the informativity proof.

Project Description

When analyzing time series data, it is often of interest to categorize them based on how different they are. We define a new dissimilarity measure between time series: Dynamic Ordered Persistence Editing (DOPE). DOPE satisfies metric properties, is stable to noise, is as informative as alternative approaches, and efficiently computable. Satisfying these properties simultaneously makes DOPE of interest to both theoreticians and data scientists alike.

Recommended Citation

Arbelo, Jose; Delgado, Antonio; Kirk, Charley; and Schlamowitz, Zach, "The DOPE Distance is SIC: A Stable, Informative, and Computable Metric on Ordered Merge Trees" (2022). Mathematics Summer Fellows. 15.
https://digitalcommons.ursinus.edu/math_sum/15