A Fast Frequent Directions Algorithm for Low Rank Approximation

Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast frequent directions algorithm for the low rank approximation prob...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence. - 1979. - 41(2019), 6 vom: 26. Juni, Seite 1279-1293
1. Verfasser: Dan Teng (VerfasserIn)
Weitere Verfasser: Chu, Delin
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2019
Zugriff auf das übergeordnete Werk:IEEE transactions on pattern analysis and machine intelligence
Schlagworte:Journal Article
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520 |a Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast frequent directions algorithm for the low rank approximation problem, which implants a randomized algorithm, sparse subspace embedding (SpEmb) in FD. This new algorithm makes use of FD's natural block structure and sends more information through SpEmb to each block in FD. We prove that our new algorithm produces a good low rank approximation with a sketch of size linear on the rank approximated. Its effectiveness and efficiency are demonstrated by the experimental results on both synthetic and real world datasets, as well as applications in network analysis 
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