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Sparse principal component analysis via axis-aligned random projections

Gataric, M; Wang, T; Samworth, RJ; (2020) Sparse principal component analysis via axis-aligned random projections. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 82 (2) pp. 329-359. 10.1111/rssb.12360. Green open access

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Abstract

We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of initialisation. We provide theoretical guarantees under which our principal subspace estimator can attain the minimax optimal rate of convergence in polynomial time. In addition, our theory provides a more refined understanding of the statistical and computational trade-off in the problem of sparse principal component estimation, revealing a subtle interplay between the effective sample size and the number of random projections that are required to achieve the minimax optimal rate. Numerical studies provide further insight into the procedure and confirm its highly competitive finite-sample performance.

Type: Article
Title: Sparse principal component analysis via axis-aligned random projections
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/rssb.12360
Publisher version: https://doi.org/10.1111/rssb.12360
Language: English
Additional information: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10087192
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