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Varshney","Krishnan Mody"],"abstract":"We propose the labeled \\v{C}ech complex, the plain labeled Vietoris-Rips\ncomplex, and the locally scaled labeled Vietoris-Rips complex to perform\npersistent homology inference of decision boundaries in classification tasks.\nWe provide theoretical conditions and analysis for recovering the homology of a\ndecision boundary from samples. 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