114 citations · 340 across the 19 of their papers we have counts for
23 papers · 1 filter
Strong Collapse of Random Simplicial Complexes
Jean-Daniel Boissonnat, Kunal Dutta, Soumik Dutta +1
The \emph{strong collapse} of a simplicial complex, proposed by Barmak and Minian (\emph{Disc. Comp. Geom. 2012}), is a combinatorial collapse of a complex onto its sub-complex. Re…
Dimensionality Reduction for Persistent Homology with Gaussian Kernels
Jean-Daniel Boissonnat, Kunal Dutta
Computing persistent homology using Gaussian kernels is useful in the domains of topological data analysis and machine learning as shown by Phillips, Wang and Zheng [SoCG 2015]. Ho…
Dimensionality Reduction for -Distance Applied to Persistent Homology
Shreya Arya, Jean-Daniel Boissonnat, Kunal Dutta +1
Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Cech filtration of P for the k-distance, and investigate the effectiveness…
Computing Persistent Homology with Various Coefficient Fields in a Single Pass
Jean-Daniel Boissonnat, Clément Maria
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-…
The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes
Jean-Daniel Boissonnat, Clément Maria
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored…
Strong Collapse for Persistence
Jean-Daniel Boissonnat, Siddharth Pritam, Divyansh Pareek
We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the…