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Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$

Abstract : We consider the problem of embedding a low-dimensional set, M, from an infinite-dimensional Hilbert space to a finite-dimensional space. Defining appropriate random linear projections, we construct a linear map which has the restricted isometry property on the secant set of M, with high probability for a number of projections essentially proportional to the intrinsic dimension of M.
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https://hal.inria.fr/hal-01157992
Contributor : Gilles Puy Connect in order to contact the contributor
Submitted on : Friday, May 29, 2015 - 11:14:01 AM
Last modification on : Thursday, January 20, 2022 - 5:28:50 PM
Long-term archiving on: : Monday, April 24, 2017 - 5:39:13 PM

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  • HAL Id : hal-01157992, version 1

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Gilles Puy, Mike E. Davies, Rémi Gribonval. Linear embeddings of low-dimensional subsets of a Hilbert space to $\mathbb{R}^m$. SPARS15 - Signal Processing with Adaptive Sparse Structured Representations, Jul 2015, Cambridge, United Kingdom. ⟨hal-01157992⟩

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