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    Alternating maximization: unifying framework for 8 sparse PCA formulations and efficient parallel codes

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    Type
    Article
    Authors
    Richtarik, Peter cc
    Jahani, Majid
    Ahipaşaoğlu, Selin Damla
    Takáč, Martin
    KAUST Department
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-09-22
    Online Publication Date
    2020-09-22
    Print Publication Date
    2021-09
    Embargo End Date
    2021-09-22
    Submitted Date
    2019-10-03
    Permanent link to this record
    http://hdl.handle.net/10754/665355
    
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    Abstract
    Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via the alternating maximization (AM) method. We show that AM is equivalent to GPower for all formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at (1) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), (2) obtaining solutions explaining more variance and (3) dealing with big data problems (our cluster code can solve a 357 GB problem in a minute).
    Citation
    Richtárik, P., Jahani, M., Ahipaşaoğlu, S. D., & Takáč, M. (2020). Alternating maximization: unifying framework for 8 sparse PCA formulations and efficient parallel codes. Optimization and Engineering. doi:10.1007/s11081-020-09562-3
    Publisher
    Springer Nature
    Journal
    Optimization and Engineering
    DOI
    10.1007/s11081-020-09562-3
    arXiv
    1212.4137
    Additional Links
    http://link.springer.com/10.1007/s11081-020-09562-3
    http://arxiv.org/pdf/1212.4137
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11081-020-09562-3
    Scopus Count
    Collections
    Articles; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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