794 citations · 896 across the 13 of their papers we have counts for
6 papers · 1 filter
Pull-back Geometry of Persistent Homology Encodings
Shuang Liang, Renata Turkeš, Jiayi Li +2
Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to p…
On the effectiveness of persistent homology
Renata Turkeš, Guido Montúfar, Nina Otter
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind i…
Alpha magnitude
Miguel O'Malley, Sara Kalisnik, Nina Otter
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encod…
Amplitudes in persistence theory
Barbara Giunti, John S. Nolan, Nina Otter +1
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants…
Stratifying multiparameter persistent homology
Heather A. Harrington, Nina Otter, Hal Schenck +1
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a…
A roadmap for the computation of persistent homology
Nina Otter, Mason A. Porter, Ulrike Tillmann +2
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbation…