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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