IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i6d10.1007_s00362-018-1045-6.html
   My bibliography  Save this article

Sparse common component analysis for multiple high-dimensional datasets via noncentered principal component analysis

Author

Listed:
  • Heewon Park

    (Yamaguchi University)

  • Sadanori Konishi

    (Chuo University)

Abstract

There is currently much discussion about the analysis of multiple datasets from different groups, among which especially identifying a common basic structure of multiple groups has drawn a large amount of attention. In order to identify a common basic structure, common component analysis (CCA) was proposed by generalizing techniques for principal component analysis (PCA); i.e., CCA becomes standard PCA when applied to only one dataset. Although CCA can identify the common structure of multiple datasets, which cannot be extracted by standard PCA, CCA suffers from the following drawbacks. The common components are estimated as linear combinations of all variables, and thus it is difficult to interpret the identified common components. The fully dense loadings lead to erroneous results in CCA, because noisy features are inevitably included in datasets. To address these issues, we incorporate sparsity into CCA, and propose a novel strategy for sparse common component analysis based on $$L_{1}$$ L 1 -type regularized regression modeling. We focus CCA which is formulated as the eigenvalue decomposition (EVD) of a Gram matrix (i.e., common loadings of multiple datasets can be estimated by EVD of a Gram matrix), and it can be performed by Singular value decomposition of a square root of the Gram matrix. We then propose sparse common component analysis based on sparse PCA to estimate sparse common loadings of multiple datasets. We also propose an algorithm to estimate sparse common loadings of multiple datasets. The proposed method can not only identify a common subspace but also select crucial common-features for multiple groups. Monte Carlo simulations and real-data analysis are conducted to examine the efficiency of the proposed sparse CCA. We observe from the numerical studies that our strategies can incorporate sparsity into the common loading estimation and efficiently recover a sparse common structure efficiently in multiple dataset analysis.

Suggested Citation

  • Heewon Park & Sadanori Konishi, 2020. "Sparse common component analysis for multiple high-dimensional datasets via noncentered principal component analysis," Statistical Papers, Springer, vol. 61(6), pages 2283-2311, December.
  • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1045-6
    DOI: 10.1007/s00362-018-1045-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-1045-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-018-1045-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boudou, A. & Cabral, E.N. & Romain, Y., 2010. "Centered and non-centered principal component analyses in the frequency domain," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 96-103, January.
    2. Paulo Rodrigues & Ana Lima, 2009. "Analysis of an European union election using principal component analysis," Statistical Papers, Springer, vol. 50(4), pages 895-904, August.
    3. Mark D McDonnell & Migel D Tissera & Tony Vladusich & André van Schaik & Jonathan Tapson, 2015. "Fast, Simple and Accurate Handwritten Digit Classification by Training Shallow Neural Network Classifiers with the ‘Extreme Learning Machine’ Algorithm," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-20, August.
    4. Jonathan A. Patz & Diarmid Campbell-Lendrum & Tracey Holloway & Jonathan A. Foley, 2005. "Impact of regional climate change on human health," Nature, Nature, vol. 438(7066), pages 310-317, November.
    5. Deniz Inan, 2015. "Combining the Liu-type estimator and the principal component regression estimator," Statistical Papers, Springer, vol. 56(1), pages 147-156, February.
    6. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iason Kynigakis & Ekaterini Panopoulou, 2022. "Does model complexity add value to asset allocation? Evidence from machine learning forecasting models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 603-639, April.
    2. Qifa Xu & Junqing Zuo & Cuixia Jiang & Yaoyao He, 2021. "A large constrained time‐varying portfolio selection model with DCC‐MIDAS: Evidence from Chinese stock market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 3417-3435, July.
    3. Thomas Conlon & John Cotter & Iason Kynigakis, 2021. "Machine Learning and Factor-Based Portfolio Optimization," Papers 2107.13866, arXiv.org.
    4. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Papers 1510.05118, arXiv.org, revised Jul 2016.
    5. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    6. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    7. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank.
    8. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    9. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    10. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    11. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    12. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    13. Dmitriy Drusvyatskiy & Adrian S. Lewis, 2018. "Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 919-948, August.
    14. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    15. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    16. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    17. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    18. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Working Papers 22-25, Federal Reserve Bank of Cleveland.
    19. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    20. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-1045-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.