IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v83y2015icp129-139.html
   My bibliography  Save this article

Multi-way PLS regression: Monotony convergence of tri-linear PLS2 and optimality of parameters

Author

Listed:
  • Hanafi, Mohamed
  • Ouertani, Samia Samar
  • Boccard, Julien
  • Mazerolles, Gérard
  • Rudaz, Serge

Abstract

The tri-linear PLS2 iterative procedure, an algorithm pertaining to the NIPALS framework, is considered. It was previously proposed as a first stage to estimate parameters of the multi-way PLS regression method. It is shown that the tri-linear PLS2 procedure is convergent. The procedure generates a sequence of parameters (scores and loadings), which can be described as increasing or decreasing two specific criteria. Furthermore, a hidden tensor is described allowing tri-linear PLS2 to search its best rank-one approximation. This tensor highlights the link between multi-way PLS regression and the well-known PARAFAC model. The parameters of the multi-way PLS regression method can be computed using three alternative procedures.

Suggested Citation

  • Hanafi, Mohamed & Ouertani, Samia Samar & Boccard, Julien & Mazerolles, Gérard & Rudaz, Serge, 2015. "Multi-way PLS regression: Monotony convergence of tri-linear PLS2 and optimality of parameters," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 129-139.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:129-139
    DOI: 10.1016/j.csda.2014.10.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314002953
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.10.003?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. T. Andrew Clayton & John C. Lindon & Olivier Cloarec & Henrik Antti & Claude Charuel & Gilles Hanton & Jean-Pierre Provost & Jean-Loïc Le Net & David Baker & Rosalind J. Walley & Jeremy R. Everett & J, 2006. "Pharmaco-metabonomic phenotyping and personalized drug treatment," Nature, Nature, vol. 440(7087), pages 1073-1077, 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. Shinji Fukuda & Yumiko Nakanishi & Eisuke Chikayama & Hiroshi Ohno & Tsuneo Hino & Jun Kikuchi, 2009. "Evaluation and Characterization of Bacterial Metabolic Dynamics with a Novel Profiling Technique, Real-Time Metabolotyping," PLOS ONE, Public Library of Science, vol. 4(3), pages 1-10, March.
    2. Nicole Bijlsma & Marc M. Cohen, 2016. "Environmental Chemical Assessment in Clinical Practice: Unveiling the Elephant in the Room," IJERPH, MDPI, vol. 13(2), pages 1-27, February.
    3. Pablo Martinez-Lozano Sinues & Malcolm Kohler & Renato Zenobi, 2013. "Human Breath Analysis May Support the Existence of Individual Metabolic Phenotypes," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-5, April.
    4. Rachel Cavill & Atanas Kamburov & James K Ellis & Toby J Athersuch & Marcus S C Blagrove & Ralf Herwig & Timothy M D Ebbels & Hector C Keun, 2011. "Consensus-Phenotype Integration of Transcriptomic and Metabolomic Data Implies a Role for Metabolism in the Chemosensitivity of Tumour Cells," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-12, March.
    5. Melissa K Friswell & Helen Gika & Ian J Stratford & Georgios Theodoridis & Brian Telfer & Ian D Wilson & Andrew J McBain, 2010. "Site and Strain-Specific Variation in Gut Microbiota Profiles and Metabolism in Experimental Mice," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-9, January.

    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:eee:csdana:v:83:y:2015:i:c:p:129-139. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.