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Rapport (Rapport Technique) Année : 2015

Linear embeddings of low-dimensional subsets of a Hilbert space to R$^m$

Résumé

We consider the problem of embedding a low-dimensional set, M, from an infinite-dimensional Hilbert space, H, to a finite-dimensional space. Defining appropriate random linear projections, we propose two constructions of linear maps that have the restricted isometry property (RIP) on the secant set of M with high probability. The first one is optimal in the sense that it only needs a number of projections essentially proportional to the intrinsic dimension of M to satisfy the RIP. The second one, which is based on a variable density sampling technique, is computationally more efficient, while potentially requiring more measurements.
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Dates et versions

hal-01116153 , version 1 (26-02-2015)
hal-01116153 , version 2 (08-06-2015)

Identifiants

  • HAL Id : hal-01116153 , version 1

Citer

Gilles Puy, Mike E. Davies, Rémi Gribonval. Linear embeddings of low-dimensional subsets of a Hilbert space to R$^m$. [Technical Report] INRIA - IRISA - PANAMA; Institute for Digital Communications (IDCom) - University of Edinburgh. 2015. ⟨hal-01116153v1⟩
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