A Multilinear Singular Value Decomposition
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Summary
There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed.
- Type
- article
- Published
- 2000-03-01
- Cited by
- 4,413
- References
- 44
- Access
- Open access
- OpenAlex
- https://openalex.org/W2013912476
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:14344372
Keywords
Multilinear map, Mathematics, Singular value decomposition, Eigenvalues and eigenvectors, Tensor (intrinsic definition)
References
- Signal Processing based on Multilinear Algebra
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- Singular Value Decomposition: a powerful concept and tool in signal processing
- SVD and signal processing: algorithms, applications and architectures
- Multiway data analysis
- Finite dimensional multilinear algebra
- Some mathematical notes on three-mode factor analysis
- Strategies for analyzing data from video fluorometric monitoring of liquid chromatographic effluents
- Kronecker Products, Unitary Matrices and Signal Processing Applications
- Matrix computations (3rd ed.)
- Blind source separation by simultaneous third-order tensor diagonalization
- Signal processing with higher-order spectra
- Decomposition of quantics in sums of powers of linear forms
- A weighted non-negative least squares algorithm for three-way ‘PARAFAC’ factor analysis
- A Decomposition for Three-Way Arrays
- Three-Mode Principal Component Analysis.
- Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors
- Independent component analysis, a survey of some algebraic methods
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- Bayesian Tensor Inference for Sketch-Based Facial Photo Hallucination
- HOSVD based image processing techniques
- A tensor higher-order singular value decomposition for integrative analysis of DNA microarray data from different studies
- Tensor-Based AAM with Continuous Variation Estimation: Application to Variation-Robust Face Recognition
- Dimension Reduction And Inferential Procedures For Images
- A Statistical Texture Model of the Liver Based on Generalized N-Dimensional Principal Component Analysis (GND-PCA) and 3D Shape Normalization
- Optical distortion evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded.
- Multilinear Sparse Principal Component Analysis
- New estimations on the upper bounds for the nuclear norm of a tensor
- Approximation of force and energy in vehicle crash using LPV type description
- Generalized principal component analysis (gpca): an algebraic geometric approach to subspace clustering and motion segmentation
- Generalized Principal Component Analysis
- A context-aware framework for personalised recommendation in mobile environments
- HOSVD Based Canonical Form for Polytopic Models of Dynamic Systems
- Integrative Statistical Learning with Applications to Predicting Features of Diseases and Health
- User behaviour modelling in a multi-dimensional environment for personalization and recommendation
- The TOPHITS Model for Higher-Order Web Link Analysis∗
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