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
Multilinear Analysis of Image Ensembles: TensorFaces
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Blind identification of convolutive MIMO systems with 3 sources and 2 sensors
EURASIP Journal on Applied Signal Processing
Higher-Order Web Link Analysis Using Multilinear Algebra
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Comments-oriented document summarization: understanding documents with readers' feedback
Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval
Two heads better than one: pattern discovery in time-evolving multi-aspect data
Data Mining and Knowledge Discovery
Probabilistic Tensor Analysis with Akaike and Bayesian Information Criteria
Neural Information Processing
Nonnegative Tensor Factorization with Smoothness Constraints
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Computing non-negative tensor factorizations
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Dynamical low-rank approximation: applications and numerical experiments
Mathematics and Computers in Simulation
Two-dimensional subspace classifiers for face recognition
Neurocomputing
Robust Simultaneous Low Rank Approximation of Tensors
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
n-Mode Singular Vector Selection in Higher-Order Singular Value Decomposition
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
MetaFac: community discovery via relational hypergraph factorization
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
An Online Approach for Mining Collective Behaviors from Molecular Dynamics Simulations
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Linear algebra for tensor problems
Computing
Hybrid clustering for validation and improvement of subject-classification schemes
Information Processing and Management: an International Journal
iOLAP: A framework for analyzing the internet, social networks, and other networked data
IEEE Transactions on Multimedia - Special section on communities and media computing
TripleRank: Ranking Semantic Web Data by Tensor Decomposition
ISWC '09 Proceedings of the 8th International Semantic Web Conference
Boosting discriminant learners for gait recognition using MPCA features
Journal on Image and Video Processing - Special issue on video-based modeling, analysis, and recognition of human motion
Singular value decompositions and low rank approximations of tensors
IEEE Transactions on Signal Processing
Human action annotation, modeling and analysis based on implicit user interaction
Multimedia Tools and Applications
Towards a matrix-based distributional model of meaning
HLT-SRWS '10 Proceedings of the NAACL HLT 2010 Student Research Workshop
A non-negative tensor factorization model for selectional preference induction
Natural Language Engineering
A survey of multilinear subspace learning for tensor data
Pattern Recognition
Nonequispaced Hyperbolic Cross Fast Fourier Transform
SIAM Journal on Numerical Analysis
Community Discovery via Metagraph Factorization
ACM Transactions on Knowledge Discovery from Data (TKDD)
Fast metadata-driven multiresolution tensor decomposition
Proceedings of the 20th ACM international conference on Information and knowledge management
Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
SIAM Journal on Scientific Computing
Plant classification based on multilinear independent component analysis
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
On revealing replicating structures in multiway data: a novel tensor decomposition approach
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Predicting RDF triples in incomplete knowledge bases with tensor factorization
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Using tensor calculus for scenario modelling
Environmental Modelling & Software
Interest prediction on multinomial, time-evolving social graphs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Sampling-free linear Bayesian update of polynomial chaos representations
Journal of Computational Physics
A New Truncation Strategy for the Higher-Order Singular Value Decomposition
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Color face tensor factorization and slicing for illumination-robust recognition
ICB'07 Proceedings of the 2007 international conference on Advances in Biometrics
MPEG video watermarking using tensor singular value decomposition
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Multi-linear data-driven dynamic hair model with efficient hair-body collision handling
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Multi-linear data-driven dynamic hair model with efficient hair-body collision handling
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
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Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor_as_matrix class supports the “matricization” of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp_tensor and tucker_tensor. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.