“dimensionality reduction”

Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets

Abstract: Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors?

Time for dithering: fast and quantized random embeddings via the restricted isometry property

Abstract: Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel geometry-preserving embeddings or to estimate the information/bits stored in this reduced data representation.