157 citations · 252 across the 26 of their papers we have counts for
7 papers · 1 filter
An improved algorithm for Generalized Čech complex construction
Jie Chu, Mikael Vejdemo-Johansson, Ping Ji
In this paper, we present an algorithm that computes the generalized Čech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this…
Multiple testing with persistent homology
Mikael Vejdemo-Johansson, Sayan Mukherjee
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the ob…
Computing minimum area homologies
Erin Wolf Chambers, Mikael Vejdemo-Johansson
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algo…
Automatic recognition and tagging of topologically different regimes in dynamical systems
Jesse Berwald, Marian Gidea, Mikael Vejdemo-Johansson
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through…
Persistence modules: Algebra and algorithms
Primoz Skraba, Mikael Vejdemo-Johansson
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistenc…
A spectral sequence for parallelized persistence
David Lipsky, Primoz Skraba, Mikael Vejdemo-Johansson
We approach the problem of the computation of persistent homology for large datasets by a divide-and-conquer strategy. Dividing the total space into separate but overlapping compon…
Interleaved computation for persistent homology
Mikael Vejdemo-Johansson
We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to…