Nonlinear estimators from ICA mixture models

Abstract Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper we assume ICAMM to derive new MAP and LMSE estimators. The first one (MAP-ICAMM) is obtained by an iterative gradient algorithm, while the second (LMSE-ICAMM) admits a closed-form solution. Both estimators can be combined by using LMSE-ICAMM to initialize the iterative computation of MAP-ICAMM .The new estimators are applied to the reconstruction of missed channels in EEG multichannel analysis. The experiments demonstrate the superiority of the new estimators with respect to: Spherical Splines, Hermite, Partial Least Squares, Support Vector Regression, and Random Forest Regression.

[1]  Xuli Han.  Direction-consistent tangent vectors for generating interpolation curves , 2019, J. Comput. Appl. Math..

[2]  David Mease,et al.  Explaining the Success of AdaBoost and Random Forests as Interpolating Classifiers , 2015, J. Mach. Learn. Res..

[3]  Ernst Fernando Lopes Da Silva Niedermeyer,et al.  Electroencephalography, basic principles, clinical applications, and related fields , 1982 .

[4]  Danilo P. Mandic,et al.  Widely linear complex partial least squares for latent subspace regression , 2018, Signal Process..

[5]  F. Torres,et al.  Electroencephalography: Basic Principles, Clinical Applications and Related Fields , 1983 .

[6]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .

[7]  Oliver Kramer,et al.  Dimensionality Reduction with Unsupervised Nearest Neighbors , 2013, Intelligent Systems Reference Library.

[8]  Wenli Jiang,et al.  Underdetermined blind separation of non-disjoint signals in time-frequency domain based on matrix diagonalization , 2011, Signal Process..

[9]  M. Manosevitz.  High-Speed Scanning in Human Memory , .

[10]  Aboul Ella Hassanien,et al.  Intelligent human emotion recognition based on elephant herding optimization tuned support vector regression , 2018, Biomed. Signal Process. Control..

[11]  G. A. Einicke,et al.  Smoothing, Filtering and Prediction - Estimating The Past, Present and Future , 2012 .

[12]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[13]  Addisson Salazar,et al.  A general procedure for learning mixtures of independent component analyzers , 2010, Pattern Recognit..

[14]  Yuedong Wang,et al.  Smoothing Splines: Methods and Applications , 2011 .

[15]  T. Ferrée,et al.  Spherical Splines and Average Referencing in Scalp Electroencephalography , 2006, Brain Topography.

[16]  Addisson Salazar.  On statistical pattern recognition in independent component analysis mixture modelling , 2012 .

[17]  Addisson Salazar,et al.  Probabilistic Distance for Mixtures of Independent Component Analyzers , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Addisson Salazar,et al.  Mixtures of independent component analyzers for microarousal detection , 2014, IEEE-EMBS International Conference on Biomedical and Health Informatics (BHI).

[19]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[20]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.