Exactly Uncorrelated Sparse Principal Component Analysis

Oh Ran Kwon, Zhaosong Lu, Hui Zou

Research output: Contribution to journalArticlepeer-review


Sparse principal component analysis (PCA) aims to find principal components as linear combinations of a subset of the original input variables without sacrificing the fidelity of the classical PCA. Most existing sparse PCA methods produce correlated sparse principal components. We argue that many applications of PCA prefer uncorrelated principal components. However, handling sparsity and uncorrelatedness properties in a sparse PCA method is nontrivial. This article proposes an exactly uncorrelated sparse PCA method named EUSPCA, whose formulation is motivated by original views and motivations of PCA as advocated by Pearson and Hotelling. EUSPCA is a non-smooth constrained non-convex manifold optimization problem. We solve it by combining augmented Lagrangian and non-monotone proximal gradient methods. We observe that EUSPCA produces uncorrelated components and maintains a similar or better level of fidelity based on adjusted total variance through simulated and real data examples. In contrast, existing sparse PCA methods produce significantly correlated components. Supplemental materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)231-241
Number of pages11
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2023 American Statistical Association and Institute of Mathematical Statistics.


  • Augmented Lagrangian method
  • Manifold optimization
  • Non-monotone proximal gradient method
  • Principal component analysis
  • Sparse principal component
  • Uncorrelated component


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