Convex Optimization
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Correntropy as a novel measure for nonlinearity tests
Signal Processing
Pattern Recognition
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
An Analysis of Unsupervised Signal Processing Methods in the Context of Correlated Sources
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Correntropy: Properties and Applications in Non-Gaussian Signal Processing
IEEE Transactions on Signal Processing
Generalized correlation function: definition, properties, and application to blind equalization
IEEE Transactions on Signal Processing - Part I
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The recently introduced correntropy function is an interesting and useful similarity measure between two random variables which has found myriad applications in signal processing. A series expansion for correntropy in terms of higher-order moments of the difference between the two random variables has been used to try to explain its statistical properties for uses such as deconvolution. We examine the existence and form of this expansion, showing that it may be divergent, e.g., when the difference has the Laplace distribution, and give sufficient conditions for its existence for differently characterized sub-Gaussian distributions. The contribution of the higher-order moments can be quite surprising, depending on the size of the Gaussian kernel in the definition of the correntropy. In the blind deconvolution setting we demonstrate that statistical exchangeability explains the existence of sub-optimal minima in the correntropy cost surface and show how the positions of these minima are controlled by the size of the Gaussian kernel.