2 citations · 2 across the 1 of their papers we have counts for
5 papers
Fuzzy simplicial sets and their application to geometric data analysis
Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad +3
In this article, we expand upon the concepts introduced by David Spivak about the relationship between the category of uber metric spaces and the category $\mathbf{sF…
Geometry and Dress groups with non-symmetric cost functions
Lukas Silvester Barth, Parvaneh Joharinad, Jürgen Jost +1
A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness rela…
Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction
Janis Keck, Lukas Silvester Barth, Fatemeh +3
Fuzzy simplicial sets have become an object of interest in dimensionality reduction and manifold learning, most prominently through their role in UMAP. However, their definition th…
Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension
Charlotte Beylier, Parvaneh Joharinad, Jürgen Jost +1
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curv…
Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization
Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad +2
Many machine learning algorithms try to visualize high dimensional metric data in 2D in such a way that the essential geometric and topological features of the data are highlighted…