8 citations · 12 across the 6 of their papers we have counts for
8 papers
Sparse Higher Order Čech Filtrations
Mickaël Buchet, Bianca B. Dornelas, Michael Kerber
For a finite set of balls of radius , the -fold cover is the space covered by at least balls. Fixing the ball centers and varying the radius, we obtain a nested sequence…
The Whole in the Parts: Putting D Persistence Modules Inside Indecomposable D Ones
Mickaël Buchet, Emerson G. Escolar
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebra…
Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
Mickaël Buchet, Emerson G. Escolar
A recent work by Lesnick and Wright proposed a visualisation of D persistence modules by using their restrictions onto lines, giving a family of D persistence modules. We giv…
On Interval Decomposability of 2D Persistence Modules
Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar +2
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the cla…
Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
Mickaël Buchet, Emerson G. Escolar
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is th…
Declutter and Resample: Towards parameter free denoising
Mickaël Buchet, Tamal K. Dey, Jiayuan Wang +1
In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth in a metric space, but it go…
Topological analysis of scalar fields with outliers
Mickaël Buchet, Frédéric Chazal, Tamal K. Dey +3
Given a real-valued function defined over a manifold embedded in , we are interested in recovering structural information about from the sole information…
Efficient and Robust Persistent Homology for Measures
Mickael Buchet, Frederic Chazal, Steve Y. Oudot +1
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is ro…