Dependence, Correlation and Gaussianity in Independent Component Analysis

By Jean-François Cardoso. 2003

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Citations in the corpus

Density Modeling of Images using a Generalized Normalization Transformation (2015, methodology): “Independent component analysis (ICA; Cardoso, 2003) can be cast in the same framework: In this case, the data x is modeled as a linear combination of independent heavy-tailed sources.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “kelihood I(fA,fV\A)− X k∈A logηk− X k∈V\A log(1 −ηk), where I(fA,fV\A) is the mutual information between two Gaussian processes (see similar reasoning in the context of independent component analysis [35]). In order to estimate A, we thus need to minimize a modular function plus a mutual information”
A Novel Ranking-Based Clustering Approach for Hyperspectral Band Selection (2016, background): “The Kurtosis of the probability distribution [44] of a band image and the Kullback–Leibler divergence [43] to its associated Gaussian probability distribution are two popular measures of non-Gaussianity.”
Sparse Modeling for Image and Vision Processing (2014, methodology): “4) or encourage the distributions of the α[j]’s to be “non-Gaussian” [Cardoso, 2003].”
Iterative Gaussianization: From ICA to Random Rotations (2011, background): “measure [25], [26], it is convenient to choose a unit covariance Gaussian as target PDF, py(y) = N (0, I).”
Cramer-Rao Lower Bound and Information Geometry (2013, background): “Another striking example, is the study of the geometry of dependence and Gaussianity for Independent Component Analysis [15].”
Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization (2009, methodology): “When � x hasfinitesecond-orderstatistics,MImaybefurtherdecomposed into two parts, representing second-order and higher-order dependencies ( Cardoso, 2004 ):”
Variational image compression with a scale hyperprior (2018, background): “Furthermore, there has been a long history of generative models, starting with independent component analysis (Cardoso, 2003), which can successfully recover factorized representations just by maximizing likelihood assuming a fully factorized prior.”