Descent Algorithms on Oblique Manifold for Source-Adaptive ICA Contrast

A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensiv...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2012-12, Vol.23 (12), p.1930-1947
Main Authors: Selvan, S. E., Amato, U., Gallivan, K. A., Chunhong Qi, Carfora, M. F., Larobina, M., Alfano, B.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Artificial intelligence
Computation
Computer science
control theory
systems
Conjugate gradient
Descent
Detection, estimation, filtering, equalization, prediction
Estimation
Exact sciences and technology
Information, signal and communications theory
Joints
Kernel
Manifolds
Mathematical analysis
Mathematical models
Normality
oblique manifold
Optimization
Parzen window
Pattern recognition. Digital image processing. Computational geometry
quasi-Newton
retraction
Signal and communications theory
Signal, noise
steepest descent
Studies
Telecommunications and information theory
vector transport
Vectors
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Summary:A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensive development of manifold techniques catering to the orthonormality constraint, only a limited number of works have been dedicated to oblique manifold ( OB ) algorithms to intrinsically handle the normality constraint, which has been empirically shown to be superior to other Riemannian and Euclidean approaches. Imposing the normality constraint implicitly, in line with the ICA definition, essentially guarantees a substantial improvement in the solution accuracy, by way of increased degrees of freedom while searching for an optimal unmixing ICA matrix, in contrast with the orthonormality constraint. Designs of the steepest descent, conjugate gradient with Hager-Zhang or a hybrid update parameter, quasi-Newton, and cost-effective quasi-Newton methods intended for OB are presented in this paper. Their performance is validated using natural images and systematically compared with the popular state-of-the-art approaches in order to assess the performance effects of the choice of algorithm and the use of a Riemannian rather than Euclidean framework. We surmount the computational challenge associated with the direct estimation of the source densities using the improved fast Gauss transform in the evaluation of the contrast function and its gradient. The proposed OB schemes may find applications in the offline image/signal analysis, wherein, on one hand, the computational overhead can be tolerated, and, on the other, the solution quality holds paramount interest.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2012.2218060