Topic
Independent component analysis
About: Independent component analysis is a research topic. Over the lifetime, 9169 publications have been published within this topic receiving 241456 citations.
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TL;DR: A novel fast algorithm for independent component analysis is introduced, which can be used for blind source separation and feature extraction, and the convergence speed is shown to be cubic.
Abstract: We introduce a novel fast algorithm for independent component analysis, which can be used for blind source separation and feature extraction. We show how a neural network learning rule can be transformed into a fixedpoint iteration, which provides an algorithm that is very simple, does not depend on any user-defined parameters, and is fast to converge to the most accurate solution allowed by the data. The algorithm finds, one at a time, all nongaussian independent components, regardless of their probability distributions. The computations can be performed in either batch mode or a semiadaptive manner. The convergence of the algorithm is rigorously proved, and the convergence speed is shown to be cubic. Some comparisons to gradient-based algorithms are made, showing that the new algorithm is usually 10 to 100 times faster, sometimes giving the solution in just a few iterations.
3,215 citations
31 Aug 2012
TL;DR: A statistical generative model called independent component analysis is discussed, which shows how sparse coding can be interpreted as providing a Bayesian prior, and answers some questions which were not properly answered in the sparse coding framework.
Abstract: Independent component models have gained increasing interest in various fields of applications in recent years. The basic independent component model is a semiparametric model assuming that a p-variate observed random vector is a linear transformation of an unobserved vector of p independent latent variables. This linear transformation is given by an unknown mixing matrix, and one of the main objectives of independent component analysis (ICA) is to estimate an unmixing matrix by means of which the latent variables can be recovered. In this article, we discuss the basic independent component model in detail, define the concepts and analysis tools carefully, and consider two families of ICA estimates. The statistical properties (consistency, asymptotic normality, efficiency, robustness) of the estimates can be analyzed and compared via the so called gain matrices. Some extensions of the basic independent component model, such as models with additive noise or models with dependent observations, are briefly discussed. The article ends with a short example.
Keywords:
blind source separation;
fastICA;
independent component model;
independent subspace analysis;
mixing matrix;
overcomplete ICA;
undercomplete ICA;
unmixing matrix
2,976 citations
TL;DR: This paper considers four different sets of allowed distortions in blind audio source separation algorithms, from time-invariant gains to time-varying filters, and derives a global performance measure using an energy ratio, plus a separate performance measure for each error term.
Abstract: In this paper, we discuss the evaluation of blind audio source separation (BASS) algorithms. Depending on the exact application, different distortions can be allowed between an estimated source and the wanted true source. We consider four different sets of such allowed distortions, from time-invariant gains to time-varying filters. In each case, we decompose the estimated source into a true source part plus error terms corresponding to interferences, additive noise, and algorithmic artifacts. Then, we derive a global performance measure using an energy ratio, plus a separate performance measure for each error term. These measures are computed and discussed on the results of several BASS problems with various difficulty levels
2,855 citations
TL;DR: A novel approach for drawing group inferences using ICA of fMRI data is introduced, and its application to a simple visual paradigm that alternately stimulates the left or right visual field is presented.
Abstract: Independent component analysis (ICA) is a promising analysis method that is being increasingly applied to fMRI data. A principal advantage of this approach is its applicability to cognitive paradigms for which detailed models of brain activity are not available. Independent component analysis has been successfully utilized to analyze single-subject fMRI data sets, and an extension of this work would be to provide for group inferences. However, unlike univariate methods (e.g., regression analysis, Kolmogorov-Smirnov statistics), ICA does not naturally generalize to a method suitable for drawing inferences about groups of subjects. We introduce a novel approach for drawing group inferences using ICA of fMRI data, and present its application to a simple visual paradigm that alternately stimulates the left or right visual field. Our group ICA analysis revealed task-related components in left and right visual cortex, a transiently task-related component in bilateral occipital/parietal cortex, and a non-task-related component in bilateral visual association cortex. We address issues involved in the use of ICA as an fMRI analysis method such as: (1) How many components should be calculated? (2) How are these components to be combined across subjects? (3) How should the final results be thresholded and/or presented? We show that the methodology we present provides answers to these questions and lay out a process for making group inferences from fMRI data using independent component analysis.
2,729 citations
TL;DR: An integrated approach to probabilistic independent component analysis for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise is presented and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses.
Abstract: We present an integrated approach to probabilistic independent component analysis (ICA) for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise. In order to avoid overfitting, we employ objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e., the number of activation and non-Gaussian noise sources. This enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data. It reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normalization of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternative-hypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and artificial FMRI data, and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses.
2,597 citations