Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI)

Sher Ali Cheema; Emilio Rafael Balda; Amir Weiss; Arie Yeredor; Martin Haardt

doi:10.1109/acssc.2017.8335434

Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI)

Sher Ali Cheema, Emilio Rafael Balda, Amir Weiss, Arie Yeredor, Martin Haardt

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Canonical Polyadic (CP) decomposition of R-way arrays is a powerful tool in multi-dimensional signal processing. There exists many methods to compute the CP decomposition. In particular, the Semi-Algebraic framework for the approximate Canonical Polyadic (CP) decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient and flexible framework for the computation of the CP decomposition. In this work, we perform a first-order performance analysis of the SECSI framework for the computation of the approximate CP decomposition of a noise corrupted low-rank 3-way tensor. We provide closed-form expressions of the relative Mean Square Factor Error (rMSFE) for each of the estimated factor matrices. The derived expressions are formulated in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. The numerical results depict the excellent match between the closed-form expressions and the empirical results.

Original language	English
Title of host publication	Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Editors	Michael B. Matthews
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	703-707
Number of pages	5
ISBN (Electronic)	9781538618233
DOIs	https://doi.org/10.1109/acssc.2017.8335434
State	Published - 2 Jul 2017
Externally published	Yes
Event	51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 - Pacific Grove, United States Duration: 29 Oct 2017 → 1 Nov 2017

Publication series

Name	Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Volume	2017-October

Conference

Conference	51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Country/Territory	United States
City	Pacific Grove
Period	29/10/17 → 1/11/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Canonical Polyadic (CP)
Perturbation analysis
tensor signal processing

Access to Document

10.1109/acssc.2017.8335434

Cite this

Cheema, S. A., Balda, E. R., Weiss, A., Yeredor, A., & Haardt, M. (2017). Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI). In M. B. Matthews (Ed.), Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 (pp. 703-707). (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017; Vol. 2017-October). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acssc.2017.8335434

Cheema, Sher Ali ; Balda, Emilio Rafael ; Weiss, Amir et al. / Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI). Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017. editor / Michael B. Matthews. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 703-707 (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017).

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abstract = "The Canonical Polyadic (CP) decomposition of R-way arrays is a powerful tool in multi-dimensional signal processing. There exists many methods to compute the CP decomposition. In particular, the Semi-Algebraic framework for the approximate Canonical Polyadic (CP) decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient and flexible framework for the computation of the CP decomposition. In this work, we perform a first-order performance analysis of the SECSI framework for the computation of the approximate CP decomposition of a noise corrupted low-rank 3-way tensor. We provide closed-form expressions of the relative Mean Square Factor Error (rMSFE) for each of the estimated factor matrices. The derived expressions are formulated in terms of the second-order moments of the noise, such that apart from a zero mean, no assumptions on the noise statistics are required. The numerical results depict the excellent match between the closed-form expressions and the empirical results.",

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Cheema, SA, Balda, ER, Weiss, A, Yeredor, A & Haardt, M 2017, Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI). in MB Matthews (ed.), Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017. Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017, vol. 2017-October, Institute of Electrical and Electronics Engineers Inc., pp. 703-707, 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017, Pacific Grove, United States, 29/10/17. https://doi.org/10.1109/acssc.2017.8335434

Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI). / Cheema, Sher Ali; Balda, Emilio Rafael; Weiss, Amir et al.
Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017. ed. / Michael B. Matthews. Institute of Electrical and Electronics Engineers Inc., 2017. p. 703-707 (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017; Vol. 2017-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Cheema SA, Balda ER, Weiss A, Yeredor A, Haardt M. Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI). In Matthews MB, editor, Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 703-707. (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017). doi: 10.1109/acssc.2017.8335434

Analytical performance analysis of the Semi-Algebraic framework for approximate CP decompositions via SImultaneous matrix diagonalizations (SECSI)

Abstract

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Bibliographical note

Keywords

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