Add to ORKGWe prove that the dynamics of the MBO scheme for data clustering converge to a viscosity solution to mean curvature flow. The main ingredients are (i) a new abstract convergence result based on quantitative estimates for heat operators and (ii) the derivation of these estimates in the setting of random geometric graphs. To implement the scheme in practice, two important parameters are the number of eigenvalues for computing the heat operator and the step size of the scheme. The results of the current paper give a theoretical justification for the choice of these parameters in relation to sample size and interaction width.Comment: Corrected typos, updated bibliograph
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Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex ...
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be ...
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In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial d...
We consider heterogeneously interacting diffusive particle systems and their large population limit....
In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial d...
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled u...
This paper is devoted to the robust approximation with a variational phase field approach of multiph...
AbstractThe convergence of the discrete graph Laplacian to the continuous manifold Laplacian in the ...
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ q...
An emerging technique in image segmentation, semi-supervised learning and general classification pro...
We analyse the properties of a semi-Lagrangian scheme for the approximation of the Mean Curvature Mo...
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We propose two related unsupervised clustering algorithms which, for input, take data assumed to be ...
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