Discriminant Analysis for Multiway Data
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.
KeywordsDiscriminant 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 ) 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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