Symposium on Discrete Geometry for Biomedical Data Analysis

On May 7, the Neural Data Representation group welcomed three guests to Tübingen for a workshop on geometric and topological methods in machine learning: Guy Wolf (Université de Montréal / Mila), Vsevolod Chernyshev (University of Ulm) and former Hertie AI Group Leader Dmitry Kobak (now at University of Ghent). The symposium brought together our group and our visitors around a shared interest in how ideas from differential geometry, harmonic analysis, and graph theory can help us make sense of complex biomedical data.

Guided data exploration with (semi-)supervised manifold learning
Guy opened the afternoon with a talk on diffusion geometry, a framework for representing data that aims to capture intrinsic structure (manifolds, neighbourhoods, smooth transitions) while factoring out the biases of how data happened to be collected. This is a recurring challenge in single-cell biology, where what we want to see — rare cell states, sparse transitions between meta-stable phenotypes — is easily drowned out by measurement noise.

Discretizations of Ricci flow in data analysis
Vsevolod followed with a talk on Ricci flow, a tool from differential geometry that deforms a manifold according to its curvature. He walked us through how this idea can be discretized on graphs (including a recent variant based on effective resistance) and turned into an algorithmic instrument for data analysis.

Discussions, and a Stocherkahn on the Neckar
After the talks, we spent the late afternoon in open discussion of ongoing projects, comparing notes, and brainstorming ideas. The day ended in proper Tübingen fashion: a pizza during a punting tour (Stocherkahn) on the Neckar, followed by drinks and dinner along the river.

The symposium was organized by Early Career Research Group Leader Sebastian Damrich:
“We’re grateful to Guy, Vsevolod, and Dmitry for making the trip, and to everyone who joined the discussions. Short, focused workshops like this one are a good reminder of how much can happen when a handful of people sit in the same room for a day.”