A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Pattern Recognition Letters
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
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
CubeSVD: a novel approach to personalized Web search
WWW '05 Proceedings of the 14th international conference on World Wide Web
Multi-Modal Tensor Face for Simultaneous Super-Resolution and Recognition
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Controlling sparseness in non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
On the convergence of bound optimization algorithms
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Estimating the spatial position of spectral components in audio
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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
Recovering tensor data from incomplete measurement via compressive sampling
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
FacetCube: a framework of incorporating prior knowledge into non-negative tensor factorization
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Probabilistic latent tensor factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Sparse non-negative tensor factorization using columnwise coordinate descent
Pattern Recognition
CIBB'10 Proceedings of the 7th international conference on Computational intelligence methods for bioinformatics and biostatistics
Uni-orthogonal nonnegative tucker decomposition for supervised image classification
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Algorithms for probabilistic latent tensor factorization
Signal Processing
SIAM Journal on Matrix Analysis and Applications
Joint training of non-negative Tucker decomposition and discrete density hidden Markov models
Computer Speech and Language
| Hi-index | 0.00 |
There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from Mørup (2007).