ICA with Orthogonality Constraint: Identifiability And A New Efficient Algorithm

Gabrielson, Ben; Akhonda, M. A. B. S.; Boukouvalas, Zois; Kim, Seung Jun

doi:10.1109/icassp39728.2021.9415059

Cited by 2 publications

(4 citation statements)

References 12 publications

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“…The result of the simulation is in line with previous work confirming that orthogonal ICA can identify independent sources [23,25,33]. Moreover, it shows that orthogonal algorithms (OgExtInf, Picard-O and FastICA) outperform equivalent nonorthogonal algorithms (ExtInf and Picard) in terms of convergence speed and convergence behavior.…”

Section: Simulated Datasupporting

confidence: 88%

“…While some algorithms as JADE or Lie group methods [22,23] maintain orthogonality intrinsically, others like FastICA require an explicit orthogonalization in each iterative step to stay in the solution space of orthogonal matrices [24]. Constraining the solution space to the orthogonal group decreases the number of independent parameters by approximately half from N 2 to N (N−1)/2 and may lead to more efficient and stable algorithms [24,25]. Orthogonal ICA has also been shown to have the same identifiability conditions as unconstrained ICA [25].…”

Section: Introductionmentioning

confidence: 99%

“…Constraining the solution space to the orthogonal group decreases the number of independent parameters by approximately half from N 2 to N (N−1)/2 and may lead to more efficient and stable algorithms [24,25]. Orthogonal ICA has also been shown to have the same identifiability conditions as unconstrained ICA [25].…”

Section: Introductionmentioning

confidence: 99%

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Orthogonal extended infomax algorithm

Ille

2024

J. Neural Eng.

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Objective. The extended infomax algorithm for independent component analysis (ICA) can separate sub- and super-Gaussian signals but converges slowly as it uses stochastic gradient optimization. In this paper, an improved extended infomax algorithm is presented that converges much faster. Approach. Accelerated convergence is achieved by replacing the natural gradient learning rule of extended infomax by a fully-multiplicative orthogonal-group based update scheme of the ICA unmixing matrix, leading to an orthogonal extended infomax algorithm (OgExtInf). The computational performance of OgExtInf was compared with original extended infomax and with two fast ICA algorithms: the popular FastICA and Picard, a preconditioned limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm belonging to the family of quasi-Newton methods. Main results. OgExtInf converges much faster than original extended infomax. For small-size electroencephalogram (EEG) data segments, as used for example in online EEG processing, OgExtInf is also faster than FastICA and Picard. Significance. OgExtInf may be useful for fast and reliable ICA, e.g. in online systems for epileptic spike and seizure detection or brain-computer interfaces.

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Section: Simulated Datasupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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Orthogonal extended infomax algorithm

Ille

2024

J. Neural Eng.

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“…, in which case orthogonality constraints can be imposed on W [k] to considerably simplify the problem [23]. For the remainder of the paper, we assume that sources and datasets are standardized, and that datasets have been pre-whitened prior to JBSS.…”

Section: Jbss Problem Formulationmentioning

confidence: 99%

An Efficient Analytic Solution for Joint Blind Source Separation

Gabrielson,

Baker Siddique Akhonda,

Lehmann

et al. 2024

IEEE Trans. Signal Process.

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Joint blind source separation (JBSS) is a powerful methodology for analyzing multiple related datasets, able to jointly extract sources that describe statistical dependencies across the datasets. However, JBSS can be computationally prohibitive with high-dimensional data, thus there exists a key need for more efficient JBSS algorithms. JBSS algorithms typically rely on numerical solutions, which may be expensive due to their iterative nature. In contrast, analytic solutions follow consistent procedures that are often less expensive. In this paper, we introduce an efficient analytic solution for JBSS. Denoting a set of sources dependent across the datasets as a "source component vector" (SCV), our solution minimizes correlation among separate SCVs by minimizing distance of the SCV cross-covariance's eigenvector matrix from a block diagonal matrix. Under the orthogonality constraint, this leads to a system of linear equations wherein each subproblem has an analytic solution. We derive identifiability conditions of our solution's estimator, and demonstrate estimation performance and time efficiency in comparison with other JBSS algorithms that exploit source correlation across datasets. Results demonstrate that our solution achieves the lowest asymptotic computational complexity among JBSS algorithms, and is capable of superior estimation performance compared with algorithms of similar complexity.

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ICA with Orthogonality Constraint: Identifiability And A New Efficient Algorithm

Cited by 2 publications

References 12 publications

Orthogonal extended infomax algorithm

Orthogonal extended infomax algorithm

An Efficient Analytic Solution for Joint Blind Source Separation

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