Tantárgy adatlapja
The goal of this course is to give an introduction to tensor networks and their application in machine learning and signal processing. With this operation we can refactorize / rewrite tensors in much smaller representation preserving the fundamental connectionis between original dimensions, in the same time either revealing hidden structures in the data or even uncovering physically interpretable terms.
Selected topics are:
- introductory examples;
- recap on basic notations, tensor diagrams, matrix and tensor operations (inner, outer, Kronecker, Khatri-Rao, etc.), norms, reshaping;
- SVD generalization to tensors: MLSVD and CPD (properties, computation and application of them);
- SVD generalization to tensor trains (TT) (properties, computation and application);
- tensors’ application on blind source separation, data fusion and ML problems;
- compelling applications from the field of biomedical signal processing (eg. epileptic seizure localization in EEG, EEG-fMRI fusion, blind deconvolution in funcional US during visual information processing).
Selected Literature:
Andrzej Cichocki, Namgil Lee, Ivan Oseledets, Anh-Huy Phan, Qibin Zhao and Danilo P. Mandic (2016), "Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions", Foundations and Trends in Machine Learning, vol. 9, no. 4-5, pp 249-429. http://dx.doi.org/10.1561/2200000059
Andrzej Cichocki, Anh-Huy Phan, Qibin Zhao, Namgil Lee, Ivan Oseledets, Masashi Sugiyama and Danilo P. Mandic (2017), "Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives", Foundations and Trends in Machine Learning, vol. 9, no. 6, pp 431-673. http://dx.doi.org/10.1561/2200000067
