Discriminant Analysis for Multiway Data

  • Gisela LechugaEmail author
  • Laurent Le Brusquet
  • Vincent Perlbarg
  • Louis Puybasset
  • Damien Galanaud
  • Arthur Tenenhaus
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 173)


A multiway Fisher Discriminant Analysis (MFDA) formulation is presented in this paper. The core of MFDA relies on the structural constraint imposed to the discriminant vectors in order to account for the multiway structure of the data. This results in a more parsimonious model than that of Fisher Discriminant Analysis (FDA) performed on the unfolded data table. Moreover, computational and overfitting issues that occur with high dimensional data are better controlled. MFDA is applied to predict the long term recovery of patients after traumatic brain injury from multi-modal brain Magnetic Resonance Imaging. As compared to FDA, MFDA clearly tracks down the discrimination areas within the white matter region of the brain and provides a ranking of the contribution of the neuroimaging modalities. Based on cross validation, the accuracy of MFDA is equal to 77 % against 75 % for FDA.


Discriminant analysis Multiway fisher discriminant analysis (MFDA) Overfitting Brain imaging 



This study was funded by a grant from the French Ministry of Health (Projet Hospitalier de Recherche Clinique registration #P051061 [2005]) and from departmental funds from the Assistance Publique-Hôpitaux de Paris. The research leading to these results has also received funding from the program “Investissements d’avenir” ANR-10-IAIHU-06 and LG acknowledges support from CONACYT.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gisela Lechuga
    • 1
    Email author
  • Laurent Le Brusquet
    • 1
  • Vincent Perlbarg
    • 2
  • Louis Puybasset
    • 3
  • Damien Galanaud
    • 4
  • Arthur Tenenhaus
    • 5
  1. 1.Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506)CentraleSupélec-CNRS-Université Paris-SudParisFrance
  2. 2.Bioinformatics/Biostatistics Platform IHU-A-ICMBrain and Spine InstituteParisFrance
  3. 3.AP-HP, Pitié-Salpêtrière HospitalDepartment of NeuroradiologyParisFrance
  4. 4.Department of Neuroradiology, AP-HPPitié-Salpêtrière Hospital, Surgical Neuro-Intensive Care UnitParisFrance
  5. 5.Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506)CentraleSupélec-CNRS-Université Paris-Sud and Bioinformatics/Biostatistics Platform IHU-A-ICM, Brain and Spine InstituteParisFrance

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