Abstract: With the rapid advances of modern technology, tensor data (i.e., multiway array) have been collected in various scientific research and engineering applications. The classification of tensor data is of great interest, where predictive models and algorithms are proposed for predicting a categorical class label for each tensor-valued sample. Aiming to improve interpretability of tensor classification methods, we consider an intuitive and efficient discriminant analysis approach, referred to as the Tucker Low-rank Classification (TLC) model. The TLC model assumes that the between-class mean differences have a low-rank Tucker decomposition, while the covariance matrix is separable. As such, the TLC model greatly reduces the number of parameters by exploiting the tensor structure. We construct a penalized estimator for the TLC model to achieve a sparse Tucker decomposition on the key discriminant analysis parameters and to further improve the parsimony in the final classifier. We establish estimation, variable selection, and prediction consistency for the penalized estimator to confirm that the proposed estimator achieves efficiency gain compared to standard methods. We demonstrate the superior performance of TLC in extensive simulation studies and real data examples.

Key words and phrases: Classification, dimension reduction, discriminant analysis, Tucker tensor decomposition