Large data limit for a phase transition model with the p-Laplacian on point clouds
2018 ◽
Vol 31
(2)
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pp. 185-231
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Keyword(s):
The consistency of a non-local anisotropic Ginzburg–Landau type functional for data classification and clustering is studied. The Ginzburg–Landau objective functional combines a double well potential, that favours indicator valued functions, and the p-Laplacian, that enforces regularity. Under appropriate scaling between the two terms, minimisers exhibit a phase transition on the order of ɛ = ɛn, where n is the number of data points. We study the large data asymptotics, i.e. as n → ∝, in the regime where ɛn → 0. The mathematical tool used to address this question is Γ-convergence. It is proved that the discrete model converges to a weighted anisotropic perimeter.
2018 ◽
Vol 149
(2)
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pp. 387-427
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Keyword(s):
2011 ◽
Vol 268-270
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pp. 811-816
Keyword(s):
Keyword(s):
2011 ◽
Vol 1
(4)
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pp. 044001
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2001 ◽
Vol 131
(3)
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pp. 567-595
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2009 ◽
Vol 61
(2)
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pp. 329-340
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