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New Persistent Cross Entropy Metric Introduced for Topological Data Analysis

By PulseAugur Editorial · [1 sources] ·

Researchers have introduced Persistent Cross Entropy (PCE), a novel method to measure the cross-entropy between two persistence diagrams. This new metric addresses the challenge of differing event spaces in persistence diagrams by using an induced probability that incorporates information from one diagram into the event space of another. PCE has demonstrated its utility in distinguishing diagrams with identical persistent entropy, identifying causal directions in dynamical systems, and serving as a directional topology loss for knowledge distillation. AI

IMPACT Introduces a new metric for topological data analysis that could enhance machine learning techniques like knowledge distillation.

RANK_REASON The item is a research paper published on arXiv detailing a new mathematical concept and its applications. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New Persistent Cross Entropy Metric Introduced for Topological Data Analysis

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The item is a research paper published on arXiv detailing a new mathematical concept and its applications. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Sijin Yeom, Jae-Hun Jung ·

    Persistent Cross Entropy

    arXiv:2608.24549v1 Announce Type: new Abstract: Persistent entropy is the Shannon entropy of a persistence-based probability measure defined on a persistence diagram. However, its cross-entropy version is not naturally defined because two persistence diagrams generally have diffe…

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