Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

[1]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[2]  Addisson Salazar,et al.  Estimating the Laplacian matrix of Gaussian mixtures for signal processing on graphs , 2018, Signal Process..

[3]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs , 2012, IEEE Transactions on Signal Processing.

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

[5]  R. Shibata,et al.  PARTIAL CORRELATION AND CONDITIONAL CORRELATION AS MEASURES OF CONDITIONAL INDEPENDENCE , 2004 .

[6]  Liming Wang,et al.  Blind Deconvolution From Multiple Sparse Inputs , 2016, IEEE Signal Processing Letters.

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

[8]  Pierre Vandergheynst,et al.  Graph Signal Processing: Overview, Challenges, and Applications , 2017, Proceedings of the IEEE.

[9]  Tao Huang,et al.  Infrared spectrum blind deconvolution algorithm via learned dictionaries and sparse representation. , 2016, Applied optics.

[10]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[11]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[12]  Pradeep Ravikumar,et al.  Sparse inverse covariance matrix estimation using quadratic approximation , 2011, MLSLP.

[13]  Pascal Frossard,et al.  Learning Laplacian Matrix in Smooth Graph Signal Representations , 2014, IEEE Transactions on Signal Processing.

[14]  W. Wu,et al.  Covariance and precision matrix estimation for high-dimensional time series , 2013, 1401.0993.

[15]  Rifai Chai,et al.  Driver Fatigue Classification With Independent Component by Entropy Rate Bound Minimization Analysis in an EEG-Based System , 2017, IEEE Journal of Biomedical and Health Informatics.

[16]  Pei Wang,et al.  Partial Correlation Estimation by Joint Sparse Regression Models , 2008, Journal of the American Statistical Association.

[17]  Addisson Salazar,et al.  Joint Conference on Neural Networks , Orlando , Florida , USA , August 12-17 , 2007 Learning Hierarchies from ICA Mixtures , 2007 .

[18]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[19]  Trevor J. Hastie,et al.  The Graphical Lasso: New Insights and Alternatives , 2011, Electronic journal of statistics.

[20]  Antonio Ortega,et al.  Graph Learning From Data Under Laplacian and Structural Constraints , 2016, IEEE Journal of Selected Topics in Signal Processing.

[21]  Addisson Salazar,et al.  On including sequential dependence in ICA mixture models , 2010, Signal Process..

[22]  Juan Manuel Górriz,et al.  Brain Connectivity Analysis: A Short Survey , 2012, Comput. Intell. Neurosci..

[23]  M. Çelebi.  General formula for conditional mean using higher order statistics , 1997 .

[24]  Ganesh R. Naik,et al.  Single channel blind source separation based local mean decomposition for Biomedical applications , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[25]  C. Croux,et al.  Robust High-Dimensional Precision Matrix Estimation , 2014, 1501.01219.

[26]  Luis Vergara,et al.  Simple approach to nonlinear prediction , 2001 .

[27]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[28]  Ganesh R. Naik,et al.  Using Blind Source Separation on accelerometry data to analyze and distinguish the toe walking gait from normal gait in ITW children , 2014, Biomed. Signal Process. Control..

[29]  Te-Won Lee,et al.  Independent Component Analysis , 1998, Springer US.

[30]  Addisson Salazar,et al.  On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods , 2014, Remote. Sens..

[31]  Antonio Soriano,et al.  Automatic credit card fraud detection based on non-linear signal processing , 2012, 2012 IEEE International Carnahan Conference on Security Technology (ICCST).

[32]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[33]  Philip A. Chou,et al.  Graph Signal Processing – A Probabilistic Framework , 2016 .

[34]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[35]  Yuejie Chi,et al.  Guaranteed Blind Sparse Spikes Deconvolution via Lifting and Convex Optimization , 2015, IEEE Journal of Selected Topics in Signal Processing.

[36]  Ganesh R. Naik,et al.  Edge Effect Elimination in Single-Mixture Blind Source Separation , 2013, Circuits, Systems, and Signal Processing.

[37]  Luis Vergara,et al.  Generalized Matched Subspace Filter for Nonindependent Noise Based on ICA , 2011, IEEE Transactions on Signal Processing.

[38]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources , 1999, Neural Comput..

[39]  Ganesh R. Naik,et al.  Single-Channel EMG Classification With Ensemble-Empirical-Mode-Decomposition-Based ICA for Diagnosing Neuromuscular Disorders , 2016, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[40]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[41]  Joshua B. Tenenbaum,et al.  Discovering Structure by Learning Sparse Graphs , 2010 .

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

[43]  Addisson Salazar,et al.  Image Applications of Agglomerative Clustering Using Mixtures of Non-Gaussian Distributions , 2015, 2015 International Conference on Computational Science and Computational Intelligence (CSCI).