Discriminant Analysis for Multi-way Data

Abstract : In standard multivariate data analysis, individuals × variables data table is usually considered (two-way data table). However, from a practical view point this simple data structure appears to be somehow limitated. It is the case for instance when individuals are charaterized by the temperature at different locations sampled over different times, leading to a three-way data structure. Such multi-way structure can be viewed as a stack of matrices X = Xi jk1≤i≤I, 1≤j≤J, 1≤k≤K from which the I horizontal slices describe the individuals i = 1, ..., I, the J lateral slices describe the variables (temperature) j = 1, ...,J and the K frontal slices describe the different time points k = 1, ...,K. Many two-way data analysis methods have been extended to the multi-way configuration. For instance, a multi-way formulation of Partial Least Squares Regression (N-PLS) has been proposed in [1]. N-PLS relies on the maximization of a covariance criterion but explicitely takes into acount the multi-way structure of the input data. In this paper, we present a Multi-way formulation of Fisher Discriminant Analysis (MFDA) in an attempt to improve the interpretability of the resulting model compared with the results obtained with unfolded methods. MFDA is illustrated on a real multi-modalMagnetic Resonance Brain Imaging (MRI) dataset
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Communication dans un congrès
PLS 2014, May 2014, Paris, France. Proceedings of the 8th International Conference on Partial Least Squares and Related Methods, 2 p., 2014
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Gisela Lechuga, Laurent Le Brusquet, Vincent Perlbarg, Louis Puybasset, Damien Galanaud, et al.. Discriminant Analysis for Multi-way Data. PLS 2014, May 2014, Paris, France. Proceedings of the 8th International Conference on Partial Least Squares and Related Methods, 2 p., 2014. 〈hal-01103853〉

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