5 papers
Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
Gary P. T. Choi, Khanh Dao Duc, Shira Faigenbaum-Golovin +6
A central objective of machine learning is to identify structure and patterns in data. Advances in data acquisition have increasingly produced datasets whose observations possess r…
VeloTree: Inferring single-cell trajectories from RNA velocity fields with varifold distances
Elodie Maignant, Tim Conrad, Christoph von Tycowicz
Trajectory inference is a critical problem in single-cell transcriptomics, which aims to reconstruct the dynamic process underlying a population of cells from sequencing data. Of p…
p-Laplacians for Manifold-valued Hypergraphs
Jo Andersson Stokke, Ronny Bergmann, Martin Hanik +1
Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we d…
Tree inference with varifold distances
Elodie Maignant, Tim Conrad, Christoph von Tycowicz
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In…
Bi-invariant Geodesic Regression with Data from the Osteoarthritis Initiative
Johannes Schade, Christoph von Tycowicz, Martin Hanik
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in…