The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms

Amir Beck*, Yakov Vaisbourd

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary coordinate-wise-based optimality condition and show its superiority over the stationarity-based condition that is commonly used in the literature, which is the basis for many of the algorithms designed to solve the problem. We devise algorithms that are based on the new optimality condition and provide numerical experiments that support our assertion that algorithms, which are guaranteed to converge to stronger optimality conditions, perform better than algorithms that converge to points satisfying weaker optimality conditions.

Original languageEnglish
Pages (from-to)119-143
Number of pages25
JournalJournal of Optimization Theory and Applications
Issue number1
StatePublished - 1 Jul 2016
Externally publishedYes


FundersFunder number
Israel Science Foundation253/12


    • Numerical methods
    • Optimality conditions
    • Principal component analysis
    • Sparsity constrained problems
    • Stationarity


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