The Tucker model with orthogonality constraints (often referred to as the HOSVD) assumes decomposition of a multi-way array into a core tensor and orthogonal factor matrices corresponding to each mode. Nonnegative Tucker Decomposition (NTD) model imposes non-negativity constraints onto both core tensor and factor matrices. In this paper, we discuss a mixed version of the models, i.e. where one factor matrix is orthogonal and the remaining factor matrices are nonnegative. Moreover, the nonnegative factor matrices are updated with the modified Barzilai-Borwein gradient projection method that belongs to a class of quasi-Newton methods. The discussed model is efficiently applied to supervised classification of facial images, hand-written digits, and spectrograms of musical instrument sounds.
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