5 citations · 7 across the 5 of their papers we have counts for
7 papers
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…
Probabilistic and nonlinear compressive sensing
Lukas Silvester Barth, Paulo von Petersenn
We present a smooth probabilistic reformulation of regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, fac…
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…
Efficient compression of neural networks and datasets
Lukas Silvester Barth, Paulo von Petersenn
Compression and generalization are fundamentally related through Solomonoff induction and the minimum description length principle (MDL), which predict that simpler models generali…
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…
IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations
Lukas Silvester Barth, Fatemeh, Fahimi +3
This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We pres…
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…