4 citations · 5 across the 2 of their papers we have counts for
8 papers
The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connection to Other Invariants
Nathaniel Clause, Woojin Kim, Facundo Mémoli
In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its app…
Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications
Tamal K. Dey, Woojin Kim, Facundo Mémoli
The notion of generalized rank invariant in the context of multiparameter persistence has become an important ingredient for defining interesting homological structures such as gen…
Bigraded Betti numbers and Generalized Persistence Diagrams
Woojin Kim, Samantha Moore
Commutative diagrams of vector spaces and linear maps over are objects of interest in topological data analysis (TDA) where this type of diagrams are called 2-parame…
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 $\…
Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics
Woojin Kim, Facundo Mémoli, Anastasios Stefanou
Metrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance between poset maps (i.e. order-pr…
Spatio-temporal Persistent Homology for Dynamic Metric Spaces
Woojin Kim, Facundo Memoli
Characterizing the dynamics of time-evolving data within the framework of topological data analysis (TDA) has been attracting increasingly more attention. Popular instances of time…