On the convergence of Jacobi-type algorithms for Independent Component Analysis
| Autor: | Pierre Comon, Konstantin Usevich, Jianze Li |
|---|---|
| Přispěvatelé: | Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong (SRIBD), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes (GIPSA-GAIA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), ANR-19-CE23-0021,LeaFleT,Apprentissage des réseaux de neurones avec des fonctions d'activation flexibles par les méthodes tensorielles(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Jacobitype algorithm
MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 02 engineering and technology Type (model theory) 01 natural sciences [SPI.AUTO]Engineering Sciences [physics]/Automatic Unitary group Convergence (routing) unitary group FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Mathematics - Numerical Analysis 0101 mathematics Mathematics orthogonal group Series (mathematics) Weak convergence 020206 networking & telecommunications Numerical Analysis (math.NA) Independent component analysis Łojasiewicz gradient inequality global convergence [STAT]Statistics [stat] independent component analysis approximate tensor diagonalization Orthogonal group weak convergence Algorithm optimization on manifold |
| Zdroj: | SAM 2020-11th Sensor Array and Multichannel Signal Processing Workshop, SAM 2020 SAM 2020-11th Sensor Array and Multichannel Signal Processing Workshop, SAM 2020, Jun 2020, Hangzhou (virtual), China. ⟨10.1109/SAM48682.2020.9104331⟩ SAM |
| DOI: | 10.1109/SAM48682.2020.9104331⟩ |
| Popis: | Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of their good performance. One natural way of choosing the index pairs in Jacobi-type algorithms is the classical cyclic ordering, while the other way is based on the Riemannian gradient in each iteration. In this paper, we mainly review in an accessible manner our recent results in a series of papers about weak and global convergence of these Jacobi-type algorithms. These results are mainly based on the Lojasiewicz gradient inequality. 5 pages |
| Databáze: | OpenAIRE |
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