Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization
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.
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Posted 11 Aug, 2020
On 04 Sep, 2020
On 08 Jul, 2020
Received 07 Jul, 2020
On 10 Jun, 2020
Received 09 Jun, 2020
Invitations sent on 08 Jun, 2020
On 08 Jun, 2020
On 03 Jun, 2020
On 02 Jun, 2020
On 02 Jun, 2020
On 26 Apr, 2020
Received 21 Apr, 2020
On 19 Mar, 2020
Received 10 Mar, 2020
Invitations sent on 09 Mar, 2020
On 09 Mar, 2020
On 07 Feb, 2020
On 06 Feb, 2020
On 06 Feb, 2020
On 06 Feb, 2020
Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization
Posted 11 Aug, 2020
On 04 Sep, 2020
On 08 Jul, 2020
Received 07 Jul, 2020
On 10 Jun, 2020
Received 09 Jun, 2020
Invitations sent on 08 Jun, 2020
On 08 Jun, 2020
On 03 Jun, 2020
On 02 Jun, 2020
On 02 Jun, 2020
On 26 Apr, 2020
Received 21 Apr, 2020
On 19 Mar, 2020
Received 10 Mar, 2020
Invitations sent on 09 Mar, 2020
On 09 Mar, 2020
On 07 Feb, 2020
On 06 Feb, 2020
On 06 Feb, 2020
On 06 Feb, 2020
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.