41 citations · 264 across the 40 of their papers we have counts for
4 papers · 1 filter
The Gaussian Transform
Kun Jin, Facundo Mémoli, Zhengchao Wan
We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a n…
On the notion of weak isometry for finite metric spaces
Alessandro De Gregorio, Ulderico Fugacci, Facundo Memoli +1
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of…
Elder-Rule-Staircodes for Augmented Metric Spaces
Chen Cai, Woojin Kim, Facundo Memoli +1
An augmented metric space is a metric space equipped with a function . This type of data arises commonly in practice, e.g, a point cloud in $\…
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Sunhyuk Lim, Facundo Memoli, Osman Berat Okutan
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information f…