4 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…
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…