Guo B, Eberly LE, Henry PG, Lenglet C, Lock EF.

Modern data often take the form of a multiway array. However, most classification methods are designed for vectors, i.e., 1-way arrays. Distance weighted discrimination (DWD) is a popular high-dimensional classification method that has been extended to the multiway context, with dramatic improvements in performance when data have multiway structure. However, the previous implementation of multiway DWD was restricted to classification of matrices, and did not account for sparsity. In this paper, the authors develop a general framework for multiway classification which is applicable to any number of dimensions and any degree of sparsity. Extensive simulation studies were conducted, showing that this model is robust to the degree of sparsity and improves classification accuracy when the data have multiway structure. Magnetic resonance spectroscopy (MRS) was used to measure the abundance of several metabolites across multiple neurological regions and across multiple time points in a mouse model of Friedreich's ataxia, yielding a four-way data array. This method reveals a robust and interpretable multi-region metabolomic signal that discriminates the groups of interest. The authors also successfully apply the method to gene expression time course data for multiple sclerosis treatment. An R implementation is available in the package MultiwayClassification at

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