A stability theorem for bigraded persistence barcodes

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.

math.AT cs.CG cs.LG math.CO math.MG Privacy-Preserving Technologies in Data Cryptography and Data Security Advanced Image and Video Retrieval Techniques

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