Frame based methods for unconstrained optimization
Journal of Optimization Theory and Applications
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Joint diagonalization via subspace fitting techniques
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 05
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Block Jacobi-type methods for non-orthogonal joint diagonalisation
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Independent component analysis by entropy bound minimization
IEEE Transactions on Signal Processing
Complex blind source separation via simultaneous strong uncorrelating transform
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Blind separation of instantaneous mixture of sources based on orderstatistics
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
On gradient adaptation with unit-norm constraints
IEEE Transactions on Signal Processing
A class of neural networks for independent component analysis
IEEE Transactions on Neural Networks
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
Independent component analysis based on nonparametric density estimation
IEEE Transactions on Neural Networks
A Minimum-Range Approach to Blind Extraction of Bounded Sources
IEEE Transactions on Neural Networks
A Unified Framework for Quadratic Measures of Independence
IEEE Transactions on Signal Processing
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It is seemingly paradoxical to the classical definition of the independent component analysis ICA, that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints to handle the inherent scaling indeterminacy of ICA but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function e.g., the absence of mixing local optima, the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search MADS method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.