Independent Component Analysis – demystified!

by Dr. Markus Plank
Scientific Consultant (Brain Products)

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For some researchers, Independent Component Analysis (ICA) to a certain extent might still be equivalent with a black box, which magically alters the data and produces “cleaner” signals. In this article, I would like to take you by the hand and demystify the theoretical background, requirements and algorithms as well as the implementation of ICA in BrainVision Analyzer 2. Of course, we cannot address all details, but at the end of this article you will certainly have a deeper understanding of the method and hopefully feel more comfortable with integrating ICA into your data processing pipelines.

Before delving into the intricacies of the method, let’s consider the following situation: A philharmonic orchestra gives a concert and you would like to record the cleanest signal possible with as little noise as possible – a challenging task since the concert hall is sold out. Wisely, you placed and securely mounted several microphones all over the concert hall, stage and rows of seats. Further, you safely assume that all the players on stage will be stationary throughout the concert (you don’t expect them to stand up and walk around while playing), and each instrument group plays their own melody. After an exciting evening, each microphone will have captured a recording of the mixed original signals, in fact you will have as many signal mixtures as you have microphones. Due to the placement of the microphones in the music hall, the mixtures will differ slightly across microphones. Now your ultimate goal is to unmix the mixture and to extract, or reconstruct, the “pure signals”. While the different melodies played by the instrument groups should of course be preserved, acoustic noise originating from the audience or – even worse – the nearby airport should be removed.

Importantly, this example can be transferred in a straightforward manner to EEG recordings. The time-domain channel activations (as represented by a time series of microvolt amplitudes) recorded from the EEG electrodes can be considered as a set of mixtures of brain signals which are supposedly generated by synchronization of neural compounds in cortex and subcortical regions, triggering far-field potentials. While the patches of neurons themselves are stationary and do not move, the activation patterns mix and merge based on the principles of volume conduction, propagate through all layers of cortex, skull, and tissue, and are ultimately present at any scalp site. Again, the ideal outcome of the analysis is to unmix this mixture, allowing for the identification of brain-based signals (which should be preserved) and non-brain signals resulting from (oculo-)motor activity, ECG or line noise (which should be removed).

In both examples, the goal is to extract the statistically “pure signals” from the recorded mixture in order to allow for a selection of signals to keep and signals to be discarded. Exactly this can be accomplished with Independent Component Analysis (ICA; Makeig et al. 1996). The technique has been recognized as a powerful tool for attenuating artifacts and analyzing statistically independent cortical processes in scalp and intracranial EEG recordings. Particularly in experimental setups where limited EEG data are available or when stereotypical artifacts such as blinks or muscular activity are contaminating the data (for example in patient groups, children or mobile EEG setups where subjects are moving freely) ICA may be superior to artifact rejection. While artifact rejection removes contaminated data portions, ICA allows for artifact attenuation, thereby preserving the original amount of samples, resulting in a higher signal-to-noise ratio for subsequent analysis steps.

ICA extracts pure signals from signal mixtures given that the following requirements are met (see Jung et al. 1998 for details):

  1. Pure signals as extracted by ICA are characterized by their time-course (melodies, neural activation patterns) which is statistically independent of any other signal. These activations in fact are the independent components (ICs).
  2. The generators of the pure signals (instrument groups, neural compounds) as well as the recording sites (microphones, electrodes) are stationary throughout the recording. Thereby the topographic projections of the components towards the recording sites are fixed.
  3. The mixing is linear and propagation delays are negligible.
  4. The probability distributions of the individual IC activations are not precisely Gaussian.

ICA does not put any further requirements on the data. In fact, it is completely agnostic of the nature of the signal, which is why ICA is generally referred to as Blind Source Separation algorithm (Hyvärinen and Oja 2000). Please keep in mind that components are purely statistical properties, so they do not map 1:1 onto physiological processes. In the context of EEG/MEG data, the extracted components can be examined based on their time-course (and topographic distribution), and components that represent noise, artifacts or other non-brain processes can be removed. Then, the corrected set of independent components is mixed or back-projected, which will result in a modified signal mixture at the electrodes where artifacts will have been attenuated.

Taken together, the transformations ICA and Inverse ICA as implemented in BrainVision Analyzer 2 are easy to use tools to diminish the effects of artifactual processes in your EEG recordings based on data-driven methods. In contrast to the previously presented transformation Ocular Correction ICA, you have the full freedom to further process and examine your data at the component level, for example by creating subnodes containing frequency- or time-frequency-domain representations of component dynamics, which may help you to determine which components to keep and which ones to remove from your data.

In the end I hope that this comprehensive introduction into ICA elicited your interest – maybe even some of my personal enthusiasm for ICA has passed onto you – and demystified the technique. While artifact correction of signals (such as speech, music or EEG) using ICA might appear to be close to magic, it is a purely statistical method which is based on certain assumptions and methodological principles, delivering a representation of temporally maximally independent component activations with temporally stable topographies.

For any further questions regarding the transformation, please contact us at support@brainproducts.com.

References
[1] Bell AJ, and Sejnowski TJ. An information-maximization approach to blind separation and blind deconvolution. Neural Comput 7: 1129-1159, 1995.
[2] Chevalier P, Albera L, Comon P, and Ferreol A. Comparative performance analysis of eight blind source separation methods on radiocommunications signals. In: International Joint Conference on Neural Networks. Budapest, Hungary: 2004.
[3] Delorme A, Palmer J, Onton J, Oostenveld R, and Makeig S. Independent EEG sources are dipolar. PLoS One 7: e30135, 2012.
[4] Delorme A, Sejnowski T, and Makeig S. Enhanced detection of artifacts in EEG data using higher-order statistics and independent component analysis. Neuroimage 34: 1443-1449, 2007.
[5] Hyvärinen A, Karhunen J, and Oja E. Indepenent Component Analysis. New York: Wiley & Sons, 2001.
[6] Hyvärinen A, and Oja E. Independent component analysis: Algorithms and applications. Neural Networks 13: 411-430, 2000.
[7] Johnson D. Colored Gaussian Noise http://cnx.org/content/m11260/latest/.
[8] Jung TP, Humphries C, Lee TW, Makeig S, McKeown MJ, Iragui V, and Sejnowski TJ. Extended ICA removes artifacts from electroencephalographic recordings. Adv Neur In 10: 894-900, 1998.
[9] Koldovsky Z, Tichavsky P, and Oja E. Efficient variant of algorithm FastICA for independent component analysis attaining the Cramer-Rao lower bound. IEEE Trans Neural Netw 17: 1265-1277, 2006.
[10] Lee TW, Girolami M, and Sejnowski TJ. Independent component analysis using an extended infomax algorithm for mixed subgaussian and supergaussian sources. Neural Comput 11: 417-441, 1999.
[11] Makeig S, Bell AJ, Jung TP, and Sejnowski TJ. Independent component analysis of electroencephalographic data. Advances in Neural Information Processing Systems 8: 145-151, 1996.
[12] Makeig S, Jung TP, Bell AJ, Ghahremani D, and Sejnowski TJ. Blind separation of auditory event-related brain responses into independent components. Proc Natl Acad Sci U S A 94: 10979-10984, 1997.
[13] Makeig S, and Onton J. ERP features and EEG dynamics: An ICA perspective. In: Oxford Handbook ofEvent‐Related Potential Components, edited by Luck S, and Kappenmann E. New York: Oxford University Press, 2008.
[14] Oja E. On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Mathematical Analysis and Applications 106: 69-84, 1985.
[15] Tipping ME, and Bishop CM. Mixtures of probabilistic principal component analyzers. Neural Comput 11: 443-482, 1999.

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