A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Numerical Analysis
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Scan Statistics on Enron Graphs
Computational & Mathematical Organization Theory
Multidimensional filtering based on a tensor approach
Signal Processing
Algorithms for sparse nonnegative tucker decompositions
Neural Computation
Incremental tensor analysis: Theory and applications
ACM Transactions on Knowledge Discovery from Data (TKDD)
Fast and Efficient Algorithms for Nonnegative Tucker Decomposition
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks, Part II
Temporal Analysis of Semantic Graphs Using ASALSAN
ICDM '07 Proceedings of the 2007 Seventh IEEE International Conference on Data Mining
Decompositions of a Higher-Order Tensor in Block Terms—Part I: Lemmas for Partitioned Matrices
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Unsupervised Multiway Data Analysis: A Literature Survey
IEEE Transactions on Knowledge and Data Engineering
SmallBlue: Social Network Analysis for Expertise Search and Collective Intelligence
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Tensor Decompositions and Applications
SIAM Review
Link Prediction on Evolving Data Using Matrix and Tensor Factorizations
ICDMW '09 Proceedings of the 2009 IEEE International Conference on Data Mining Workshops
Hierarchical ALS algorithms for nonnegative matrix and 3D tensor factorization
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
A two stage algorithm for K-mode convolutive nonnegative tucker decomposition
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Efficient penetration depth approximation using active learning
ACM Transactions on Graphics (TOG)
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Analysis of high dimensional data in modern applications, such as neuroscience, text mining, spectral analysis, chemometrices naturally requires tensor decomposition methods. The Tucker decompositions allow us to extract hidden factors (component matrices) with different dimension in each mode, and investigate interactions among various modalities. The alternating least squares (ALS) algorithms have been confirmed effective and efficient in most of tensor decompositions, especially Tucker with orthogonality constraints. However, for nonnegative Tucker decomposition (NTD), standard ALS algorithms suffer from unstable convergence properties, demand high computational cost for large scale problems due to matrix inverse, and often return suboptimal solutions. Moreover they are quite sensitive with respect to noise, and can be relatively slow in the special case when data are nearly collinear. In this paper, we propose a new algorithm for nonnegative Tucker decomposition based on constrained minimization of a set of local cost functions and hierarchical alternating least squares (HALS). The developed NTD-HALS algorithm sequentially updates components, hence avoids matrix inverse, and is suitable for large-scale problems. The proposed algorithm is also regularized with additional constraint terms such as sparseness, orthogonality, smoothness, and especially discriminant. Extensive experiments confirm the validity and higher performance of the developed algorithm in comparison with other existing algorithms.