IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v9y2015i3p267-286.html
   My bibliography  Save this article

Probabilistic auto-associative models and semi-linear PCA

Author

Listed:
  • Serge Iovleff

Abstract

Auto-associative models cover a large class of methods used in data analysis, including for example principal component analysis (PCA) and auto-associative neural networks. In this paper, we describe the general properties of these models when the projection component is linear and we propose and test an easy-to-implement probabilistic semi-linear auto-associative model in a Gaussian setting. We show that it is a generalization of the PCA model to the semi-linear case. Numerical experiments on simulated datasets and a real astronomical application highlight the interest of this approach. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Serge Iovleff, 2015. "Probabilistic auto-associative models and semi-linear PCA," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 267-286, September.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:3:p:267-286
    DOI: 10.1007/s11634-014-0185-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11634-014-0185-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11634-014-0185-3?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. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
    2. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    3. Durand, Jean-Francois, 1993. "Generalized principal component analysis with respect to instrumental variables via univariate spline transformations," Computational Statistics & Data Analysis, Elsevier, vol. 16(4), pages 423-440, October.
    4. Girard, Stéphane & Iovleff, Serge, 2005. "Auto-associative models and generalized principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 21-39, March.
    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. Girard, Stéphane & Iovleff, Serge, 2005. "Auto-associative models and generalized principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 21-39, March.
    2. Pedro Delicado & Mario Huerta, 2003. "Principal Curves of Oriented Points: theoretical and computational improvements," Computational Statistics, Springer, vol. 18(2), pages 293-315, July.
    3. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    4. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    5. Dorota Toczydlowska & Gareth W. Peters & Man Chung Fung & Pavel V. Shevchenko, 2017. "Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components," Risks, MDPI, vol. 5(3), pages 1-77, July.
    6. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    7. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    8. Wang, Shao-Hsuan & Huang, Su-Yun, 2022. "Perturbation theory for cross data matrix-based PCA," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    9. Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Wentao Qu & Xianchao Xiu & Huangyue Chen & Lingchen Kong, 2023. "A Survey on High-Dimensional Subspace Clustering," Mathematics, MDPI, vol. 11(2), pages 1-39, January.
    11. Ligon, Ethan, 2017. "Estimating household welfare from disaggregate expenditures," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5gc4h1fm, Department of Agricultural & Resource Economics, UC Berkeley.
    12. Jiaju Miao & Pawel Polak, 2023. "Online Ensemble of Models for Optimal Predictive Performance with Applications to Sector Rotation Strategy," Papers 2304.09947, arXiv.org.
    13. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    14. Marconi, Gabriele, 2014. "European higher education policies and the problem of estimating a complex model with a small cross-section," MPRA Paper 87600, University Library of Munich, Germany.
    15. Jingying Yang, 2024. "Element Aggregation for Estimation of High-Dimensional Covariance Matrices," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    16. Dimitris Korobilis & Maximilian Schroder, 2022. "Probabilistic quantile factor analysis," Papers 2212.10301, arXiv.org, revised Dec 2022.
    17. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.
    18. Jung, WoongHee & Taflanidis, Alexandros A., 2023. "Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    19. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Sep 2023.
    20. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.

    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:advdac:v:9:y:2015:i:3:p:267-286. 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.