The Ring of Algebraic Functions on Persistence Bar Codes

2013/04/02 by Adcock, Aaron, Carlsson, Erik, Carlsson, Gunnar · 3 citations
#13Pxx #68T10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1304.0530

Abstract

We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.

Cited by

• Topological Feature Extraction of Scanty Time Series Data: A Data-Driven Approach for Dynamic State Change Detection
• From Betti Numbers to Persistence Diagrams: A Hybrid Quantum Algorithm for Topological Data Analysis
• Topological Machine Learning with Unreduced Persistence Diagrams

Related

• Stabilization of codimension of persistence barcodes
• A Theory of Sub-Barcodes
• An isometry theorem for persistent homology of circle-valued functions
• Computation of γ-linear projected barcodes for multiparameter persistence
• Exterior Critical Series of Persistence Modules