Paper#Topological Data Analysis, Persistent Homology, Outlier Robustness🔬 ResearchAnalyzed: Jan 3, 2026 15:46
Robust Persistent Homology with Trimming
Published:Dec 30, 2025 13:36
•1 min read
•ArXiv
Analysis
This paper introduces a robust version of persistent homology, a topological data analysis technique, designed to be resilient to outliers. The core idea is to use a trimming approach, which is particularly relevant for real-world datasets that often contain noisy or erroneous data points. The theoretical analysis provides guarantees on the stability of the proposed method, and the practical applications in simulated and biological data demonstrate its effectiveness.
Key Takeaways
- •Proposes a robust version of persistent homology using a trimming approach.
- •Addresses the issue of outliers both inside and outside the data cloud.
- •Provides theoretical guarantees on the stability of the method.
- •Demonstrates the practicality of the method with simulated and real-world biological data.
Reference
“The methodology works when the outliers lie outside the main data cloud as well as inside the data cloud.”