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Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization
Adam Borowicz
Corresponding Author
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View the published version at EURASIP Journal on Advances in Signal Processing.
Independent component analysis (ICA) is a popular technique for demixing multi-channel data. The performance of a typical ICA algorithm strongly depends on the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often a linear mixing model is assumed and source signals are extracted by data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a novel algorithm, based on the quaternionic factorization of rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits $4 \times 4$ rotation matrices and uses approximate negentropy as a contrast function. Consequently, the proposed method can be adjusted to a given data distribution (e.g. super-Gaussians) by selecting a suitable non-linear function that approximates the negentropy. Compared to the widely-used, the symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and is more accurate in the presence of multiple Gaussian sources.
Keywords
BSS, ICA, Jacobi rotations, negentropy, quaternions
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CURRENT STATUS: Published
Version 2
Posted 11 Aug, 2020
Published
On 04 Sep, 2020
No community comments so far
Editorial decision: Accept
On 08 Jul, 2020
Review #2 received
Received 07 Jul, 2020
Reviewer #2 agreed
On 10 Jun, 2020
Review #1 received
Received 09 Jun, 2020
Reviewers invited
Invitations sent on 08 Jun, 2020
Reviewer #1 agreed
On 08 Jun, 2020
Editor assigned
On 03 Jun, 2020
Submission checks complete
On 02 Jun, 2020
Editor invited
On 02 Jun, 2020
No comments provided
Editorial decision: Major revision
On 26 Apr, 2020
Review #2 received
Received 21 Apr, 2020
Reviewer #2 agreed
On 19 Mar, 2020
Review #1 received
Received 10 Mar, 2020
Reviewers invited
Invitations sent on 09 Mar, 2020
Reviewer #1 agreed
On 09 Mar, 2020
Editor assigned
On 07 Feb, 2020
First submitted
On 06 Feb, 2020
Submission checks complete
On 06 Feb, 2020
Editor invited
On 06 Feb, 2020
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Subject Areas
Theoretical Computer Science
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This preprint is under consideration at EURASIP Journal on Advances in Signal Processing. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research
Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization
Adam Borowicz
Corresponding Author
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Published
Version 2
Posted 11 Aug, 2020
Published
On 04 Sep, 2020
No community comments so far
Editorial decision: Accept
On 08 Jul, 2020
Review #2 received
Received 07 Jul, 2020
Reviewer #2 agreed
On 10 Jun, 2020
Review #1 received
Received 09 Jun, 2020
Reviewers invited
Invitations sent on 08 Jun, 2020
Reviewer #1 agreed
On 08 Jun, 2020
Editor assigned
On 03 Jun, 2020
Submission checks complete
On 02 Jun, 2020
Editor invited
On 02 Jun, 2020
No comments provided
Editorial decision: Major revision
On 26 Apr, 2020
Review #2 received
Received 21 Apr, 2020
Reviewer #2 agreed
On 19 Mar, 2020
Review #1 received
Received 10 Mar, 2020
Reviewers invited
Invitations sent on 09 Mar, 2020
Reviewer #1 agreed
On 09 Mar, 2020
Editor assigned
On 07 Feb, 2020
First submitted
On 06 Feb, 2020
Submission checks complete
On 06 Feb, 2020
Editor invited
On 06 Feb, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Theoretical Computer Science
License:
This work is licensed under a CC BY 4.0 License. Read Full License
View the published version at EURASIP Journal on Advances in Signal Processing.
Independent component analysis (ICA) is a popular technique for demixing multi-channel data. The performance of a typical ICA algorithm strongly depends on the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often a linear mixing model is assumed and source signals are extracted by data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a novel algorithm, based on the quaternionic factorization of rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits $4 \times 4$ rotation matrices and uses approximate negentropy as a contrast function. Consequently, the proposed method can be adjusted to a given data distribution (e.g. super-Gaussians) by selecting a suitable non-linear function that approximates the negentropy. Compared to the widely-used, the symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and is more accurate in the presence of multiple Gaussian sources.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.