Approximate Matrix Multiplication with Application to Linear Embeddings

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of the nuclear norm over the spectral norm. The presented bound has improved dependence with respect to the approximation error (as compared to previous approaches), whereas the subspace - on which we project the input matrices - has dimensions proportional to the maximum of their nuclear rank and it is independent of the input dimensions. In addition, we provide an application of this result to linear low-dimensional embeddings. Namely, we show that any Euclidean point-set with bounded nuclear rank is amenable to projection onto number of dimensions that is independent of the input dimensionality, while achieving additive error guarantees.

Published in:
2014 Ieee International Symposium On Information Theory (Isit), 2182-2186
Presented at:
IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, JUN 29-JUL 04, 2014
New York, Ieee

 Record created 2015-04-13, last modified 2018-09-13

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