Tensor techniques in signal processing: algorithms for the canonical polyadic decomposition (PARAFAC)

• Main Author: Silva, Alex Pereira da
• Other Authors: Mota, João César Moura
• Language: English
• Published: 2016
• Subjects: Teleinformática; Tensor (Cálculo); Deflação
• Online Access: http://www.repositorio.ufc.br/handle/riufc/19361

SILVA, A. P. Tensor techniques in signal processing: algorithms for the canonical polyadic decomposition (PARAFAC). 2016. 124 f. Tese (Doutorado em Engenharia de Teleinformática) - Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2016. === Submitted by Marlene Sousa ([e-mail]) on 2016-09-01T18:41:38Z No. of bitstreams: 1 2016_tese_apsilva.pdf: 1648271 bytes, checksum: be3747d533837939c3a410d2f017ddfa (MD5) === Approved for entry into archive by Marlene Sousa ([e-mail]) on 2016-09-01T18:42:06Z (GMT) No. of bitstreams: 1 2016_tese_apsilva.pdf: 1648271 bytes, checksum: be3747d533837939c3a410d2f017ddfa (MD5) === Made available in DSpace on 2016-09-01T18:42:06Z (GMT). No. of bitstreams: 1 2016_tese_apsilva.pdf: 1648271 bytes, checksum: be3747d533837939c3a410d2f017ddfa (MD5) Previous issue date: 2016-06-29 === Low rank tensor decomposition has been playing for the last years an important role in many applications such as blind source separation, telecommunications, sensor array processing, neuroscience, chemometrics, and data mining. The Canonical Polyadic tensor decomposition is very attractive when compared to standard matrix-based tools, manly on system identification. In this thesis, we propose: (i) several algorithms to compute specific low rank-approximations: finite/iterative rank-1 approximations, iterative deflation approximations, and orthogonal tensor decompositions. (ii) A new strategy to solve multivariate quadratic systems, where this problem is reduced to a best rank-1 tensor approximation problem. (iii) Theoretical results to study and proof the performance or the convergence of some algorithms. All performances are supported by numerical experiments