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• W3127409101 abstract "We consider a problem of great practical interest: the repairing and recovery of a low-dimensional manifold embedded in high-dimensional space from noisy scattered data. Suppose that we observe a point cloud sampled from the low-dimensional manifold, with noise, and let us assume that there are holes in the data. Can we recover missing information inside the holes? While in low-dimension the problem was extensively studied, manifold repairing in high dimension is still an open problem. We introduce a new approach, called Repairing Manifold Locally Optimal Projection (R-MLOP), that expands the MLOP method introduced by Faigenbaum-Golovin et al. in 2020, to cope with manifold repairing in low and high-dimensional cases. The proposed method can deal with multiple holes in a manifold. We prove the validity of the proposed method, and demonstrate the effectiveness of our approach by considering different manifold topologies, for single and multiple holes repairing, in low and high dimensions." @default.
• W3127409101 created "2021-02-15" @default.
• W3127409101 creator A5068471566 @default.
• W3127409101 creator A5087100604 @default.
• W3127409101 date "2021-02-02" @default.
• W3127409101 modified "2023-09-27" @default.
• W3127409101 title "Manifold Repairing, Reconstruction and Denoising from Scattered Data in High-Dimension." @default.
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• W3127409101 hasPublicationYear "2021" @default.
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