An Immune-Inspired, Dependence-Based Approach to Blind Inversion of Wiener Systems

In this work, we present a comparative analysis of two methods — based on the autocorrelation and autocorrentropy functions — for representing the time structure of a given signal in the context of the unsupervised inversion of Wiener systems by Hammerstein systems. Linear stages with and without feedback are considered and an immune-inspired algorithm is used to allow parameter optimization without the need for manipulating the cost function, and also with a significant probability of global convergence. The results indicate that both functions provide effective means for system inversion and also illustrate the effect of linear feedback on the overall system performance.

[1]  Jugurta R. Montalvão Filho,et al.  An immune-inspired, information-theoretic framework for blind inversion of Wiener systems , 2015, Signal Process..

[2]  Stergios B. Fotopoulos,et al.  Discrete-Time Dynamic Models , 2001, Technometrics.

[3]  Fernando José Von Zuben,et al.  Nonlinear Blind Source Deconvolution Using Recurrent Prediction-Error Filters and an Artificial Immune System , 2009, ICA.

[4]  Yingbo Hua,et al.  Optimal Design of Non-Regenerative MIMO Wireless Relays , 2007, IEEE Transactions on Wireless Communications.

[5]  Alireza K. Ziarani,et al.  A nonlinear adaptive method of elimination of power line interference in ECG signals , 2002, IEEE Transactions on Biomedical Engineering.

[6]  Jose C. Principe,et al.  Information Theoretic Learning - Renyi's Entropy and Kernel Perspectives , 2010, Information Theoretic Learning.

[7]  B. Peeters,et al.  Stochastic System Identification for Operational Modal Analysis: A Review , 2001 .

[8]  Shengli Xie,et al.  Online Blind Source Separation Using Incremental Nonnegative Matrix Factorization With Volume Constraint , 2011, IEEE Transactions on Neural Networks.

[9]  Stefan M. Moser,et al.  A Student's Guide to Coding and Information Theory: List of contributors , 2012 .

[10]  Bernard Widrow,et al.  Adaptive Inverse Control: A Signal Processing Approach , 2007 .

[11]  Deniz Erdoğmuş,et al.  Towards a unification of information theoretic learning and kernel methods , 2004, Proceedings of the 2004 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing, 2004..

[12]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[13]  Gerald Sommer,et al.  A hyperbolic multilayer perceptron , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[14]  A C den Brinker A comparison of results from parameter estimations of impulse responses of the transient visual system. , 1989, Biological cybernetics.

[15]  Christian Jutten,et al.  Quasi-nonparametric blind inversion of Wiener systems , 2001, IEEE Trans. Signal Process..

[16]  Jordi Solé i Casals,et al.  A Fast Gradient Approximation for Nonlinear Blind Signal Processing , 2012, Cognitive Computation.

[17]  Deniz Erdoğmuş,et al.  Blind source separation using Renyi's mutual information , 2001, IEEE Signal Processing Letters.

[18]  Paul A. Viola,et al.  Empirical Entropy Manipulation for Real-World Problems , 1995, NIPS.

[19]  Deniz Erdogmus,et al.  An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems , 2002, IEEE Trans. Signal Process..

[20]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[21]  S. Laughlin,et al.  The rate of information transfer at graded-potential synapses , 1996, Nature.

[22]  A Mahalanobis,et al.  Optimal trade-off synthetic discriminant function filters for arbitrary devices. , 1994, Optics letters.

[23]  John G. Proakis Intersymbol Interference in Digital Communication Systems , 2003 .

[24]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[25]  João Marcos Travassos Romano,et al.  Blind Source Separation of Post-Nonlinear Mixtures Using Evolutionary Computation and Gaussianization , 2009, ICA.

[26]  José Carlos Príncipe,et al.  Generalized correlation function: definition, properties, and application to blind equalization , 2006, IEEE Transactions on Signal Processing.

[27]  Dimitrios Hatzinakos,et al.  Blind identification of linear subsystems of LTI-ZMNL-LTI models with cyclostationary inputs , 1997, IEEE Trans. Signal Process..

[28]  Deniz Erdogmus,et al.  Information Theoretic Learning , 2005, Encyclopedia of Artificial Intelligence.

[29]  Dimitris G. Manolakis,et al.  Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing , 1999 .

[30]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixture of sources based on order statistics , 2000, IEEE Trans. Signal Process..

[31]  Christian Jutten,et al.  Blind Inversion of Wiener System using a minimization-projection (MP) approach , 2003 .

[32]  Michel Verleysen,et al.  Mutual information for the selection of relevant variables in spectrometric nonlinear modelling , 2006, ArXiv.

[33]  Roberto Battiti,et al.  Using mutual information for selecting features in supervised neural net learning , 1994, IEEE Trans. Neural Networks.

[34]  Igor Vajda,et al.  Estimation of the Information by an Adaptive Partitioning of the Observation Space , 1999, IEEE Trans. Inf. Theory.

[35]  Dinh-Tuan Pham,et al.  Fast approximation of nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems , 2005, Signal Process..

[36]  José Carlos Príncipe,et al.  Information theoretic learning with adaptive kernels , 2011, Signal Process..

[37]  Ricardo Suyama,et al.  Unsupervised Signal Processing , 2010 .

[38]  Fernando José Von Zuben,et al.  Learning and optimization using the clonal selection principle , 2002, IEEE Trans. Evol. Comput..

[39]  Christian Jutten,et al.  Parametric approach to blind deconvolution of nonlinear channels , 2002, ESANN.

[40]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: Wiener and Hammerstein cascade models , 1986, Biological Cybernetics.

[41]  John Wright,et al.  RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[42]  Lai-Wan Chan,et al.  Practical method for blind inversion of Wiener systems , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[43]  Yucai Zhu Identification of Hammerstein models for control using ASYM , 2000 .

[44]  Carlos García Puntonet,et al.  An Evolutionary Approach for Blind Inversion of Wiener Systems , 2007, ICA.

[45]  S. Haykin Adaptive Filters , 2007 .

[46]  A. Rényi On Measures of Entropy and Information , 1961 .

[47]  Wlodzimierz Greblicki,et al.  Nonlinearity estimation in Hammerstein systems based on ordered observations , 1996, IEEE Trans. Signal Process..