Laux, Tim and Lelmi, Jona (2023) Large data limit of the MBO scheme for data clustering: convergence of the dynamics. JOURNAL OF MACHINE LEARNING RESEARCH, 24: 344. ISSN 1532-4435,
Full text not available from this repository. (Request a copy)Abstract
We 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE METHODS; THRESHOLD DYNAMICS; MEAN-CURVATURE; SPECTRAL CONVERGENCE; VISCOSITY SOLUTIONS; GRAPH LAPLACIANS; HEAT KERNEL; MOTION; SEGMENTATION; FLOW; Graph MBO; clustering; semi-supervised learning; continuum limits; viscosity solutions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Apr 2024 13:06 |
| Last Modified: | 22 Apr 2024 13:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/62593 |
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