A stability theorem for bigraded persistence barcodes
arXiv:2303.14694v37 citationsh-index: 24
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This work addresses theoretical foundations in topological data analysis, likely incremental as it extends existing persistence methods to a bigraded setting.
The authors tackled the problem of defining and proving stability for bigraded persistence barcodes in topological data analysis, resulting in a stability theorem for these structures derived from the moment-angle complex of Vietoris-Rips filtrations.
We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes.