Constrained Least Squares for Extended Complex Factor Analysis

Ahmad Mouri Sardarabadi; Alle-Jan van der Veen; L.V.E. Koopmans

doi:10.1109/SAM.2018.8448962

Constrained Least Squares for Extended Complex Factor Analysis

Ahmad Mouri Sardarabadi, Alle-Jan van der Veen, L.V.E. Koopmans

Signal Processing Systems

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

For subspace estimation with an unknown colored noise, Factor Analysis (FA) and its extensions, denoted as Extended FA (EFA), are good candidates for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in (E)FA can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for (E)FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.

Original language	English
Title of host publication	2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)
Publisher	IEEE
Pages	169-173
Number of pages	5
ISBN (Electronic)	978-1-5386-4752-3
ISBN (Print)	978-1-5386-4753-0
DOIs	https://doi.org/10.1109/SAM.2018.8448962
Publication status	Published - 2018
Event	10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018 - Sheffield, United Kingdom Duration: 8 Jul 2018 → 11 Jul 2018 Conference number: 10

Conference

Conference	10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018
Country/Territory	United Kingdom
City	Sheffield
Period	8/07/18 → 11/07/18

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Factor Analysis
Non-Linear Optimization
Covariance Matching

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08448962Final published version, 333 KB

https://ieeexplore.ieee.org/document/8448962

Cite this

@inproceedings{a0f4a67e9c65486fbe921a548ac4aa77,

title = "Constrained Least Squares for Extended Complex Factor Analysis",

abstract = "For subspace estimation with an unknown colored noise, Factor Analysis (FA) and its extensions, denoted as Extended FA (EFA), are good candidates for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in (E)FA can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for (E)FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.",

keywords = "Factor Analysis, Non-Linear Optimization, Covariance Matching",

author = "{Mouri Sardarabadi}, Ahmad and {van der Veen}, Alle-Jan and L.V.E. Koopmans",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. ; 10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018 ; Conference date: 08-07-2018 Through 11-07-2018",

year = "2018",

doi = "10.1109/SAM.2018.8448962",

language = "English",

isbn = "978-1-5386-4753-0 ",

pages = "169--173",

booktitle = "2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)",

publisher = "IEEE",

address = "United States",

}

Mouri Sardarabadi, A, van der Veen, A-J & Koopmans, LVE 2018, Constrained Least Squares for Extended Complex Factor Analysis. in 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM). IEEE, pp. 169-173, 10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018, Sheffield, United Kingdom, 8/07/18. https://doi.org/10.1109/SAM.2018.8448962

TY - GEN

T1 - Constrained Least Squares for Extended Complex Factor Analysis

AU - Mouri Sardarabadi, Ahmad

AU - van der Veen, Alle-Jan

AU - Koopmans, L.V.E.

N1 - Conference code: 10

PY - 2018

Y1 - 2018

N2 - For subspace estimation with an unknown colored noise, Factor Analysis (FA) and its extensions, denoted as Extended FA (EFA), are good candidates for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in (E)FA can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for (E)FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.

AB - For subspace estimation with an unknown colored noise, Factor Analysis (FA) and its extensions, denoted as Extended FA (EFA), are good candidates for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in (E)FA can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for (E)FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.

KW - Factor Analysis

KW - Non-Linear Optimization

KW - Covariance Matching

U2 - 10.1109/SAM.2018.8448962

DO - 10.1109/SAM.2018.8448962

M3 - Conference contribution

SN - 978-1-5386-4753-0

SP - 169

EP - 173

BT - 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)

PB - IEEE

T2 - 10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018

Y2 - 8 July 2018 through 11 July 2018

ER -

Constrained Least Squares for Extended Complex Factor Analysis

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Keywords

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