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Sparse principal component analysis via axis‐aligned random projections
Author(s) -
Gataric Milana,
Wang Tengyao,
Samworth Richard J.
Publication year - 2020
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12360
Subject(s) - principal component analysis , minimax , estimator , initialization , sparse pca , mathematical optimization , covariance matrix , eigenvalues and eigenvectors , subspace topology , mathematics , rate of convergence , computer science , covariance , algorithm , component (thermodynamics) , artificial intelligence , statistics , physics , thermodynamics , computer network , channel (broadcasting) , quantum mechanics , programming language
Summary 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 it is not vulnerable to a bad choice of initialization. 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.