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A consistency theorem for randomized singular value decomposition

Author

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  • Chen, Ting-Li
  • Huang, Su-Yun
  • Wang, Weichung

Abstract

The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for developing efficient large-scale SVD algorithms. Randomized SVD was proposed, and its potential was demonstrated for computing a low-rank SVD (Rokhlin et al., 2009). In this article, we introduce a consistency notion for random projections used in randomized SVD and provide a consistency theorem for it. We also present a numerical example to show how the random projections to low dimension affect the consistency.

Suggested Citation

  • Chen, Ting-Li & Huang, Su-Yun & Wang, Weichung, 2020. "A consistency theorem for randomized singular value decomposition," Statistics & Probability Letters, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s0167715220300468
    DOI: 10.1016/j.spl.2020.108743
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