An Augmented Echo State Network for Nonlinear Adaptive Filtering of Complex Noncircular Signals

A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signal...

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Bibliographic Details
Published in:IEEE transactions on neural networks 2011-01, Vol.22 (1), p.74-83
Main Authors: Yili Xia, Jelfs, B, Van Hulle, M M, Principe, J C, Mandic, D P
Format: Article
Language:English
Subjects:
Adaptation model
Algorithms
Applied sciences
Artificial Intelligence
Augmented complex statistics
Benchmark testing
complex noncircularity
Computer science
control theory
systems
Computer Simulation
Computer systems and distributed systems. User interface
Connectionism. Neural networks
Covariance matrix
echo state networks
Exact sciences and technology
Information retrieval. Graph
Mathematical Concepts
Neural Networks (Computer)
Neurons
Nonlinear dynamical systems
Nonlinear Dynamics
Pattern Recognition, Automated - standards
Signal Processing, Computer-Assisted
Software
Theoretical computing
Training
Vectors
Weather
widely linear modeling
Wind
wind prediction
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Summary:A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signals, both second-order circular (proper) and noncircular (improper). Next, in order to deal with nonstationary processes with large nonlinear dynamics, a nonlinear readout layer is introduced and is further equipped with an adaptive amplitude of the nonlinearity. This combination of augmented complex statistics and enhanced adaptivity within ESNs also facilitates the processing of bivariate signals with strong component correlations. Simulations in the prediction setting on both circular and noncircular synthetic benchmark processes and real-world noncircular and nonstationary wind signals support the analysis.
ISSN:1045-9227
1941-0093
DOI:10.1109/TNN.2010.2085444