A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Facial Expression Decomposition
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
Numerische Mathematik
Face transfer with multilinear models
ACM SIGGRAPH 2005 Papers
Handwritten digit classification using higher order singular value decomposition
Pattern Recognition
Algorithms for sparse nonnegative tucker decompositions
Neural Computation
Computational Intelligence and Neuroscience - Advances in Nonnegative Matrix and Tensor Factorization
Tensor Decompositions and Applications
SIAM Review
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
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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 nonnegativity 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.