Concepts of linear algebra are generalized to higher-order tensors. This includes investigating how key matrix decompositions, like the singular value decomposition, can be generalized to tensors. Numerical algorithms are derived. Tensor tools are used to develop new techniques for signal processing and data analysis, such as algorithms for independent component analysis and multi-way factor analysis. Some specific applications (mainly in biomedical engineering and wireless communication) are studied in more detail.
Keywords: linear and multilinear algebra, numerical algorithms, statistical signal and array processing, higher-order statistics, independent component analysis and blind source separation, harmonic retrieval, factor analysis, blind identification and equalization.
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Some data sets are available as well.
Workshop on Tensor Decompositions and Applications (TDA 2010), Sept. 13-17, 2010, Monopoli, Bari, Italy.
Special Issue of the SIAM Journal on Matrix Analysis and Applications on Tensor Decompositions and Applications.
Lieven De Lathauwer K.U.Leuven Campus Kortrijk Group Science, Engineering and Technology E. Sabbelaan 53 8500 Kortrijk Belgium T: +32-56-24.60.62 F: +32-56-24.69.99 E: Lieven dot DeLathauwer at kuleuven-kortrijk dot be K.U.Leuven - E.E. Dept. (ESAT) - SCD-SISTA Kasteelpark Arenberg 10, bus 2446 B-3001 Leuven-Heverlee Belgium T: +32-16-32.86.63 F: +32-16-32.19.70 E: Lieven dot DeLathauwer at esat dot kuleuven dot be