Elements of information theory
Elements of information theory
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Adaptive blind separation of independent sources: a deflation approach
Signal Processing
The Minimum Entropy and Cumulants Based Contrast Functions for Blind Source Extraction
IWANN '01 Proceedings of the 6th International Work-Conference on Artificial and Natural Neural Networks: Bio-inspired Applications of Connectionism-Part II
Dependence, correlation and Gaussianity in independent component analysis
The Journal of Machine Learning Research
A Mathematical Theory of Communication
A Mathematical Theory of Communication
Signal Processing - Special issue: Information theoretic signal processing
Blind separation of instantaneous mixture of sources based on orderstatistics
IEEE Transactions on Signal Processing
Independent component analysis based on nonparametric density estimation
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Signal Processing - Special issue: Information theoretic signal processing
Spectral analysis of seasonality in tourism demand
Mathematics and Computers in Simulation
Zero-Entropy minimization for blind extraction of bounded sources (BEBS)
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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The marginal entropy h(Z) of a weighted sum of two variables Z = αX + βY, expressed as a function of its weights, is a usual cost function for blind source separation (BSS), and more precisely for independent component analysis (ICA). Even if some theoretical investigations were done about the relevance from the BSS point of view of the global minimum of h(Z), very little is known about possible local spurious minima.In order to analyze the global shape of this entropy as a function of the weights, its analytical expression is derived in the ideal case of independent variables. Because of the ICA assumption that distributions are unknown, simulation results are used to show how and when local spurious minima may appear. Firstly, the entropy of a whitened mixture, as a function of the weights and under the constraint of independence between the source variables, is shown to have only relevant minima for ICA if at most one of the source distributions is multimodal. Secondly, it is shown that if independent multimodal sources are involved in the mixture, spurious local minima may appear. Arguments are given to explain the existence of spurious minima of h(Z) in the case of multimodal sources. The presented justification can also explain the location of these minima knowing the source distributions. Finally, it results from numerical examples that the maximum-entropy mixture is not necessarily reached for the 'most mixed' one (i.e. equal mixture weights), but depends of the entropy of the mixed variables.