TL;DR
This paper investigates the algebraic structure of functions on persistence barcodes to enhance pattern recognition techniques in topological data analysis.
Contribution
It introduces a novel algebraic framework for analyzing persistence barcodes, enabling new methods for data pattern recognition.
Findings
Developed a ring of algebraic functions on barcodes
Applied the framework to improve pattern recognition
Provided theoretical insights into barcode algebraic structures
Abstract
We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.
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