arXiv Open Access 2022

Large data limit of the MBO scheme for data clustering: convergence of the dynamics

Tim Laux Jona Lelmi

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.AP math.NA math.ST

Penulis (2)

Tim Laux

Jona Lelmi

Format Sitasi

APA MLA BibTeX

Laux, T., Lelmi, J. (2022). Large data limit of the MBO scheme for data clustering: convergence of the dynamics. https://arxiv.org/abs/2209.05837

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓