期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 69, 期 -, 页码 2218-2232出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2021.3066258
关键词
Matrix decomposition; Approximation algorithms; Signal processing algorithms; Sparse matrices; Singular value decomposition; Signal processing; Oceanography; Low-rank approximation; rank-revealing matrix factorization; the pivoted QLP; the singular value decomposition; randomized numerical linear algebra
资金
- National Key Research and Development Program of China [2018AAA0102200]
- 111 project [B18041]
A new algorithm called PbP-QLP is introduced in this paper for efficiently approximating low-rank matrices without using pivoting strategy, which allows it to leverage modern computer architectures better than competing randomized algorithms. The efficiency and effectiveness of PbP-QLP are demonstrated through various classes of synthetic and real-world data matrices.
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is computationally prohibitive for large matrices. In this paper, we introduce a new algorithm termed Projection-based Partial QLP (PbP-QLP) that efficiently approximates the p-QLP with high accuracy. Fundamental in our work is the exploitation of randomization and in contrast to the p-QLP, PbP-QLP does not use the pivoting strategy. As such, PbP-QLP can harness modern computer architectures, even better than competing randomized algorithms. The efficiency and effectiveness of our proposed PbP-QLP algorithm are investigated through various classes of synthetic and real-world data matrices.
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