次高斯矩阵的逼近性约化：一个统一理论
Dimensionality reduction with subgaussian matrices: a unified theory
摘要：
我们提出了一个理论，欧几里德降维与亚高斯矩阵，统一了几个限制等距属性和约翰逊-林登施特劳斯型的结果，以前获得的特定数据集。特别是，我们恢复，并在几种情况下，提高结果集的稀疏和结构稀疏向量，低秩矩阵和张量，光滑流形。此外，我们建立了一个新的Johnson-Lindenstrauss嵌入的数据集的形式的Hilbert空间的子空间的无限联盟。
英文摘要：
We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured sparse vectors, low-rank matrices and tensors, and smooth manifolds. In addition, we establish a new Johnson-Lindenstrauss embedding for data sets taking the form of an infinite union of subspaces of a Hilbert space.
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