Correntropy: Properties and Applications in Non-Gaussian Signal Processing

The optimality of second-order statistics depends heavily on the assumption of Gaussianity. In this paper, we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure. A close relationship between correntropy and M-estim...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2007-11, Vol.55 (11), p.5286-5298
Main Authors: Weifeng Liu, Pokharel, P.P., Principe, J.C.
Format: Article
Language:English
Subjects:
Applied sciences
Bandwidth
Exact sciences and technology
Gaussian processes
Generalized correlation function
information theoretic learning
Information theory
Information, signal and communications theory
Joints
Kernel
kernel methods
Kernels
Mean square error methods
metric
Miscellaneous
Non-Gaussian
Optimization
Probability theory
Random processes
Random variables
Robustness
Signal processing
Similarity
Statistics
Telecommunications and information theory
temporal principal component analysis (TPCA)
Yield estimation
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Summary:The optimality of second-order statistics depends heavily on the assumption of Gaussianity. In this paper, we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure. A close relationship between correntropy and M-estimation is established. Connections and differences between correntropy and kernel methods are presented. As such correntropy has vastly different properties compared with second-order statistics that can be very useful in non-Gaussian signal processing, especially in the impulsive noise environment. Examples are presented to illustrate the technique.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.896065