Graph methods for machine learning have been found to be extraordinarily successful in several imaging and data analysis applications. They aim to build a graph from the data by encoding similarities between elements and use possible non-local similarity measures for comparison, clustering and classification. The study of large-data limits of state-of-the-art graph models such as Ginzburg-Landau functionals, Cheeger cuts etc. is fundamental for the design of efficient optimisation strategies. In this mini-symposium we gather experts in the field of mathematical graph modelling and large-data convergence to highlight analogies and differences between continuum and discrete variational models for data analysis.

Scaling Results in Lp Regularised Semi-Supervised Learning

Matthew Thorpe (University of Cambridge)

Discrete to continuum limit of the graph Ginzburg-Landau functional

Yves van Gennip (University of Nottingham)

Gromov-Hausdorff limit of Wasserstein spaces on point clouds

Garcia Trillos Nicolas (Brown University)

Large data and zero noise limits of graph-based semi-supervised learning algorithms

Matt Dunlop (Caltech)

Organizers:

Luca Calatroni (CMAP, École Polytechnique CNRS)

Daniel Tenbrinck (University of Münster)

Matthew Thorpe (University of Cambridge)

Keywords:

bayesian methods, graphical methods, image reconstruction, image segmentation, machine learning, partial differential equation models