f4e3ce3e7b581ff32e40968298ba013d-AuthorFeedback.pdf

RelationtoTDA.5 Indeed, a persistent-homology-based loss was the first thing we tried! Unfortunately, the noisy classifier as a filter6 function was not very helpful. We ended up using the label as the filter function and the algorithm evolved into its7 currentform. Yes, our method works in the ambient space with similar guarantees on purity.13 However,the abundancycould be limited; the largest component for labeliwill still be pure, but could be small as14 itonly covers one (the largest) piece ofthe true region oflabeli(in whichηi 1/2).