Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration

arXiv:2204.07821v3 Announce Type: replace-cross
Abstract: A novel topological-data-analytical (TDA) method is proposed to distinguish, from noise, small holes surrounded by high-density regions of a probability density function. The proposed method is robust against additive noise and outliers. Traditional TDA tools, like those based on the distance filtration, often struggle to distinguish small features from noise, because both have short persistences. An alternative filtration, called the Robust Density-Aware Distance (RDAD) filtration, is proposed to prolong the persistences of small holes of …

abstract arxiv cs.cg data detection function math.at math.st noise novel outliers probability robust scale small stat.ml stat.th tools type