A consistency theorem for randomized singular value decomposition

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

Statistics & Probability Letters, 2020, vol. 161, issue C

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.

Keywords: Consistency; Randomized algorithm; Singular value decomposition; Principal component analysis (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108743

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