An Improved Frequent Directions Algorithm for Low-Rank Approximation via Block Krylov Iteration

Frequent directions (FDs), as a deterministic matrix sketching technique, have been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality but experiences a lot of computational cost for large-scale data. Several recent works on the randomiz...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 35; no. 7; pp. 9428 - 9442
Main Authors: Wang, Chenhao, Yi, Qianxin, Liao, Xiuwu, Wang, Yao
Format: Journal Article
Language:English
Published: United States IEEE 01.07.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Accuracy
Algorithms
Approximation
Approximation algorithms
Approximation error
Block Krylov iteration
Computational efficiency
Computer applications
Computing costs
Cost analysis
Costs
Efficiency
Error analysis
frequent directions (FDs)
low-rank approximation
Neural networks
Principal component analysis
randomized sketching
Signal processing algorithms
Sparse matrices
streaming algorithms
Theoretical analysis
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:Frequent directions (FDs), as a deterministic matrix sketching technique, have been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality but experiences a lot of computational cost for large-scale data. Several recent works on the randomized version of FDs greatly improve the computational efficiency but unfortunately sacrifice some precision. To remedy such an issue, this article aims to find a more accurate projection subspace to further improve the efficiency and effectiveness of the existing FDs' techniques. Specifically, by utilizing the power of the block Krylov iteration and random projection technique, this article presents a fast and accurate FDs algorithm named r-BKIFD. The rigorous theoretical analysis shows that the proposed r-BKIFD has a comparable error bound with original FDs, and the approximation error can be arbitrarily small when the number of iterations is chosen appropriately. Extensive experimental results on both synthetic and real data further demonstrate the superiority of r-BKIFD over several popular FDs algorithms both in terms of computational efficiency and accuracy.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2022.3233243