Persistent Cross Entropy Extends Topological Data Analysis
Key takeaways
- Persistent Cross Entropy (PCE) extends cross-entropy to persistence diagrams.
- It bridges different event spaces using an induced probability measure.
- PCE can distinguish diagrams with identical persistent entropy.
- It enables causal direction separation and serves as a topology loss for knowledge distillation.
Who benefits
Summary
This paper introduces Persistent Cross Entropy (PCE), a novel extension of cross-entropy to persistence diagrams, which are used in topological data analysis. PCE bridges different event spaces of diagrams using an induced probability, enabling new applications like distinguishing diagrams with similar persistent entropy and separating causal directions in dynamical systems.
Why it matters
Professionals working with complex, high-dimensional data in fields like materials science, biology, or finance can leverage PCE to gain deeper insights into data structure, causality, and for more robust knowledge distillation in machine learning models.
How to implement this in your domain
- 1Explore the application of topological data analysis (TDA) and persistence diagrams in current data analysis workflows.
- 2Investigate how Persistent Cross Entropy (PCE) can be used to compare and distinguish complex data structures.
- 3Apply PCE to analyze causal relationships in time-series data or dynamical systems within your domain.
- 4Consider using PCE as a novel loss function for knowledge distillation in machine learning models, particularly for preserving topological features.
- 5Collaborate with TDA experts to integrate PCE into advanced data science projects.
Original post by Sijin Yeom, Jae-Hun Jung
"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…"
View on XOriginally posted by Sijin Yeom, Jae-Hun Jung on X · view source
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