High-Order Contrasts for Independent Component Analysis

By Jean-François Cardoso. 1999

Subfields: Statistics and Probability, Representation & Self-Supervised Learning, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

1. Francis R. Bach
2. Arthur Gretton
3. Bernhard Schölkopf
4. Kenji Fukumizu
5. Michael I. Jordan
6. Gerry Leversha
7. Bharath K. Sriperumbudur
8. Martin J. Wainwright

In Representation & Self-Supervised Learning

1. Bernhard Schölkopf
2. Francis R. Bach
3. Michael I. Jordan
4. Kenji Fukumizu
5. Arthur Gretton
6. Eric Learned-Miller
7. Siwei Lyu
8. Peter J. Bickel

In Signal Processing

1. Bernhard Schölkopf
2. Aapo Hyvärinen
3. Francis R. Bach
4. Arthur Gretton
5. Michael I. Jordan
6. Eero P. Simoncelli
7. Gerry Leversha
8. Siwei Lyu

Citations in the corpus

• Rethinking LDA: Moment Matching for Discrete ICA (2015, neutral): “We explain how we initialize the parameter c 0 for the LDA moments in Appendix G.3.”
• Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization (2009, methodology): “…Mallat & Zhang, 1993; Olshausen & Field, 1997; Chen, Donoho, & Saunders, 1998; Lewicki & Sejnowski, 2000; Donoho & Elad, 2003). the expected value of a higher-order contrast function to avoid the diffi-culties associated with entropy estimation (Comon, 1994; Bell & Sejnowski, 1997; Cardoso, 1999).”
• Canonical Correlation Analysis Applied to Remove Muscle Artifacts From the Electroencephalogram (2006, methodology): “• ICA: as it is not in the scope of this paper to compare all different ICA algorithms, we limited ourself to the Joint Approximate Diagonalization of Eigen-matrices (JADE) algorithm [12], previously used in two studies for muscle artifact removal in scalp EEG recordings [4], [13].”
• ICA Using Spacings Estimates of Entropy (2003, methodology): “Our tests included comparisons with FastICA [11], the JADE algorithm [12], the extended Infomax algorithm [13], and KernelICA using the generalized variance [10].”
• Convolutive Speech Bases and Their Application to Supervised Speech Separation (2007, methodology): “employed the JADE algorithm [16] in our simulations).”
• Kernel-Based Nonlinear Blind Source Separation (2003, methodology): “8 We use the algorithm described in Cardoso and Souloumiac (1996). See also Cardoso (1999) .”
• Measure Transformed Independent Component Analysis (2013, background): “…Sejnowski, 1995; Lee et al., 1999; Pham and Garat, 1999; Koldovsky et al., 2006; Todros and Tabrikian, 2007), on non-Gaussianity measures such as kurtosis (Hyvärinen and Oja, 1997), or on high-order correlations such as fourth-order cross-cumulants (Cardoso and Souloumiac, 1993; Cardoso, 1999).”
• Kernel independent component analysis (2003, methodology): “Unfortunately, the mutual information for real-valued variables is difficult to approximate and optimize on the basis of a finite sample, and much research on ICA has focused on alternative contrast functions [8, 7, I].”
• Saliency, attention, and visual search: an information theoretic approach. (2009, unknown): “An encoding based on ICA is optimal with respect to the statistics of the natural environment and therefore there is some representation of natural image statistics in general inherent in the context specific model in the definition of the receptive fields themselves.”
• Time-domain blind audio source separation using advanced ICA methods (2007, methodology): “Direct utilization of ICA for the audio BSS is not possible, because most of ICA algorithms [4, 2] are designed for instantaneous mixtures, where no delays are considered (Mij = 0 ∀i, j).”
• Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators (2013, background): “Whereas higher order statistics can provide helpful tools in specific contexts [15], and have been extensively used in system identification, causal inference and blind source separation (see for example [10, 13, 5]); it is difficult to derive a general approach with solid theoretical results accoun”
• Independent Component Analysis of Climate Data: A New Look at EOF Rotation (2009, background): “It is common in practice to approximate these contrasts using higher-order cumulants (Cardoso 1999).”
• Statistical Inference for Independent Component Analysis: Application to Structural VAR Models (2017, methodology): “…with a focus on the numerical convergence and computational complexity of the algorithm used to get the estimate [see e.g. Amari, Cardoso (1997), Cardoso (1999), Cardoso, Laheld (1996), Cardoso, Souloumiac (1993), Comon (1994), Sections 4.2, 4.3., Hyvarinen (1997), Section 6, Hyvarinen (1999),…”
• Efficient independent component analysis (2006, methodology): “and normal [3] lognormal(1, 1) [11] mixture Gaussians: multimodal [4] t(5) [12] mixture Gaussians: unimodal [5] logistic(0, 1) [13] exp(1) vs. normal(0,1) [6] Weibull(3, 1) [14] lognormal(1, 1) vs. normal(0, 1) [ 7 ] exp(10) + normal(0, 1) [15] Weibull(3, 1) vs. exp(1) 2836 A. CHEN AND P. J. BICKEL”