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348
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract

Cited by 1492 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
An informationmaximization approach to blind separation and blind deconvolution
 NEURAL COMPUTATION
, 1995
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Fast and robust fixedpoint algorithms for independent component analysis
 IEEE TRANS. NEURAL NETW
, 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
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Cited by 511 (34 self)
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Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informationtheoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixedpoint algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
The "Independent Components" of Natural Scenes are Edge Filters
, 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
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Cited by 477 (27 self)
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It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attempts to find a factorial code of independent visual features. We show here that a new unsupervised learning algorithm based on information maximization, a nonlinear "infomax" network, when applied to an ensemble of natural scenes produces sets of visual filters that are localized and oriented. Some of these filters are Gaborlike and resemble those produced by the sparsenessmaximization network. In addition, the outputs of these filters are as independent as possible, since this infomax network performs Independent Components Analysis or ICA, for sparse (supergaussian) component distributions. We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zerophase whitening filters (ZCA). The ICA filters have more sparsely distributed (kurtotic) outputs on natural scenes. They also resemble the receptive fields of simple cells in visual cortex, which suggests that these neurons form a natural, informationtheoretic
A fast fixedpoint algorithm for independent component analysis
 Neural Computation
, 1997
"... Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fixed ..."
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Cited by 429 (19 self)
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Abstract. Independent Subspace Analysis (ISA; Hyvarinen & Hoyer, 2000) is an extension of ICA. In ISA, the components are divided into subspaces and components in different subspaces are assumed independent, whereas components in the same subspace have dependencies.In this paper we describe a fixedpoint algorithm for ISA estimation, formulated in analogy to FastICA. In particular we give a proof of the quadratic convergence of the algorithm, and present simulations that confirm the fast convergence, but also show that the method is prone to convergence to local minima. 1
Survey of clustering algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 231 (3 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
Independent Factor Analysis
 Neural Computation
, 1999
"... We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square no ..."
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Cited by 219 (9 self)
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We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing, but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a twostep procedure. In the first step, the source densities, mixing matrix and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectationmaximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of Gaussians, thus all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear ...
Independent Component Analysis Using an Extended Infomax Algorithm for Mixed SubGaussian and SuperGaussian Sources
, 1999
"... An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able to blindly separate mixed signals with sub and superGaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a pro ..."
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Cited by 202 (21 self)
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An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able to blindly separate mixed signals with sub and superGaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have suband superGaussian regimes were used to derive a general learning rule that preserves the simple architecture proposed by Bell and Sejnowski (1995), is optimized using the natural gradient by Amari (1998), and uses the stability analysis of Cardoso and Laheld (1996) to switch between sub and superGaussian regimes. We demonstrate that the extended infomax algorithm is able to easily separate 20 sources with a variety of source distributions. Applied to highdimensional data from electroencephalographic (EEG) recordings, it is effective at separating artifacts such as eye blinks and line noise from weaker electrical ...
Analysis of fMRI Data by Blind Separation Into Independent Spatial Components
 Human Brain Mapping
, 1998
"... : Current analytical techniques applied to functional magnetic resonance imaging (fMRI) data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Here we describe a new method for analyzing fMRI data based on the independent ..."
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Cited by 161 (16 self)
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: Current analytical techniques applied to functional magnetic resonance imaging (fMRI) data require a priori knowledge or specific assumptions about the time courses of processes contributing to the measured signals. Here we describe a new method for analyzing fMRI data based on the independent component analysis (ICA) algorithm of Bell and Sejnowski ([1995]: Neural Comput 7:11291159). We decomposed eight fMRI data sets from 4 normal subjects performing Stroop colornaming, the Brown and Peterson word/number task, and control tasks into spatially independent components. Each component consisted of voxel values at fixed threedimensional locations (a component "map"), and a unique associated time course of activation. Given data from 144 time points collected during a 6min trial, ICA extracted an equal number of spatially independent components. In all eight trials, ICA derived one and only one component with a time course closely matching the time course of 40sec alternat...