A New Non-archimedean Metric on Persistent Homology

arXiv:2012.02655 · math.AT, cs.LG, stat.ML · Submitted 2020-12-04 · Read on arXiv

math.AT, cs.LG, stat.ML

Submitted: 2020-12-04

Updated: 2021-12-07

Comments: 18 pages, 6 figures

Journal ref: Computational Statistics 2022

DOI: 10.1007/s00180-021-01187-z

Code: https://github.com/ismailguzel/TDA-HC

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Clustering — 63× in this paper · explained in 2 episodes
• Persistent Homology — 59× in this paper · explained in 3 episodes
• Homogeneity — 7× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Cosine Similarity — 2× in this paper · explained in 3 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Topological Data Analysis (TDA) — 1× in this paper · explained in 2 episodes
• alpha — 1× in this paper · explained in 1 episode

Sources

• Persistent Clustering and a Theorem of J. Kleinberg
• Persistence Curves: A canonical framework for summarizing persistence diagrams
• The mergegram of a dendrogram and its stability
• Intrinsic Hierarchical Clustering Behavior Recovers Higher Dimensional Shape Information

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