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Found 8 papers, 2 papers with code
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
In particular, we show the discrete eigenvalues and eigenvectors converge to their continuum analogues at a dimension-dependent rate, which allows us to interpret the efficacy of discrete spectral clustering using Fermat distances in terms of the resulting continuum limit.
It begins with a boundary: A geometric view on probabilistically robust learning
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples.
Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks
In our framework, the fusion occurs in a layer-wise manner and builds on an interpretation of a node in a network as a function of the layer preceding it.
Rates of Convergence for Regression with the Graph Poly-Laplacian
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation.
The Geometry of Adversarial Training in Binary Classification
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional.
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum levels.
A variational approach to the consistency of spectral clustering
We also show that the discrete clusters obtained via spectral clustering converge towards a continuum partition of the ground truth measure.
Continuum limit of total variation on point clouds
We consider point clouds obtained as random samples of a measure on a Euclidean domain.
