Optimal low-rank QR decomposition with an application on RP-TSOD

Research output: Chapter in Book/Conference proceedingBook Chapterpeer-review


Low-rank matrix approximation has many applications, e.g., denoising, recommender systems and image reconstruction. Recently, a Randomized Pivoted Two-Sided Orthogonal Decomposition (RP-TSOD) was developed to exploit the randomization in approximating a high-dimensional matrix using QR decomposition. Instead of random projection, we propose to optimize the projection matrix for low-rank QR decomposition with the target of minimizing the approximation error. A method based on gradient descent is developed to derive optimal projections. The developed techniques can be used in not only RP-TSOD, but also other decompositions. Experimental results on both synthetic data and real data show that the proposed method could more accurately approximate a high-dimensional matrix than RP-TSOD.
Original languageEnglish
Title of host publicationNeural Information Processing
Subtitle of host publication30th International Conference, ICONIP 2023, Changsha, China, November 20–23, 2023, Proceedings, Part XIV
EditorsBiao Luo, Long Cheng, Zheng-Guang Wu, Hongyi Li, Chaojie Li
Place of PublicationSingapore
PublisherSpringer Nature Singapore
ISBN (Electronic)9789819981816
Publication statusPublished - 27 Nov 2023

Publication series

NameCommunications in Computer and Information Science


  • Low-rank matrix approximation
  • optimal projection
  • QR decomposition


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