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304
Probabilistic Independent Component Analysis
, 2003
"... Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ..."
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Cited by 205 (14 self)
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Independent Component Analysis is becoming a popular exploratory method for analysing complex data such as that from FMRI experiments. The application of such 'modelfree' methods, however, has been somewhat restricted both by the view that results can be uninterpretable and by the lack of ability to quantify statistical significance. We present an integrated approach to Probabilistic ICA for FMRI data that allows for nonsquare mixing in the presence of Gaussian noise. We employ an 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 nonGaussian noise sources. Reduction of the data to this 'true' subspace before the ICA decomposition automatically results in an estimate of the noise, leading to the ability to assign significance to voxels in ICA spatial maps. Estimation of the number of intrinsic sources not only enables us to carry out probabilistic modelling, but also achieves an asymptotically unique decomposition of the data. This 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 normafisation 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 alternativehypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and complex artificial FMRI data, and compared to the spatiotemporal accuracy of restfits obtaine...
Regional homogeneity approach to fMRI data analysis
 NeuroImage
, 2004
"... Kendall’s coefficient concordance (KCC) can measure the similarity of a number of time series. It has been used for purifying a given cluster in functional MRI (fMRI). In the present study, a new method was developed based on the regional homogeneity (ReHo), in which KCC was used to measure the simi ..."
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Cited by 87 (10 self)
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Kendall’s coefficient concordance (KCC) can measure the similarity of a number of time series. It has been used for purifying a given cluster in functional MRI (fMRI). In the present study, a new method was developed based on the regional homogeneity (ReHo), in which KCC was used to measure the similarity of the time series of a given voxel to those of its nearest neighbors in a voxelwise way. Six healthy subjects performed left and right finger movement tasks in eventrelated design; five of them were additionally scanned in a rest condition. KCC was compared among the three conditions (left finger movement, right finger movement, and the rest). Results show that bilateral primary motor cortex (M1) had higher KCC in either left or right finger movement condition than in rest condition. Contrary to prediction and to activation pattern, KCC of ipsilateral M1 is significantly higher than contralateral M1 in unilateral finger movement conditions. These results support the previous electrophysiologic findings of increasing ipsilateral M1 excitation during unilateral movement. ReHo can consider as a complementary method to modeldriven method, and it could help reveal the complexity of the human brain function. More work is needed to understand the neural mechanism underlying ReHo.
Imaging brain dynamics using independent component analysis
 Proceedings of the IEEE
"... The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signal ..."
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Cited by 75 (25 self)
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The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signals from these recordings. A similar approach is proving useful for analyzing functional magnetic resonance brain imaging (fMRI) data. In this paper, we outline the assumptions underlying ICA and demonstrate its application to a variety of electrical and hemodynamic recordings from the human brain. Keywords—Blind source separation, EEG, fMRI, independent component analysis.
Survey of Sparse and NonSparse Methods in Source Separation
, 2005
"... Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sour ..."
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Cited by 51 (1 self)
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Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. When the information about the mixing process and sources is limited, the problem is called ‘blind’. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that solutions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous nonsparse methods. Indeed, sparse methods provide a powerful approach to the separation of linear mixtures of independent data. This paper surveys the recent arrival of sparse blind source separation methods and the previously existing nonsparse methods, providing insights and appropriate hooks into the literature along the way.
Unmixing fMRI with Independent Component Analysis  Using ICA to Characterize HighDimensional fMRI Data in a Concise Manner
, 2006
"... Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. Typically, it assumes a generative model where observations are assumed to be linear mixtu ..."
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Cited by 41 (17 self)
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Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. Typically, it assumes a generative model where observations are assumed to be linear mixtures of independent sources, and unlike principal component analysis (PCA), which uncorrelates the data, ICA works with higherorder statistics to achieve independence. An intuitive example of ICA can be given by a scatterplot of two independent signals s1 and s2. Figure 1(a) shows a plot of the two independent signals (s1, s2) in a scatter plot. Figure 1(b) and (c) shows the projections for PCA and ICA, respectively, for a linear mixture of s1 and s2. PCA finds the orthogonal vectors u1, u2 but does not find independent vectors. In contrast, ICA is able to find the independent vectors a1, a2 of the linear mixed signals (s1, s2) and is thus able to restore the original sources. A typical ICA model assumes that the source signals are not observable, are statistically independent, and are nonGaussian, with an unknown but linear mixing process. Consider an observed Mdimensional random vector denoted by x = (x1,... xM) T, which is generated by the ICA model: x = As, (1) where s = [s1, s2,... sN] T is an Ndimensional vector whose elements are assumed independent sources and AM×N is an unknown mixing matrix. Typically M> = N, so A is usually of full rank. The goal of ICA is to estimate an unmixing matrix WN×M such that y [defined in (2)] is a good approximation to the true sources: s. y = Wx (2) ICA is hence an approach to solving the blind source separation problem, which traditionally addresses the solution of the cocktail party problem in which several people are speaking simultaneously in the same room. The problem is to separate the voices of the different speakers by using recordings of several microphones in the room [2]. The basic ICA model for blind source separation is shown
Detection of consistently taskrelated activation in fMRI data with hybrid independent component analysis. NeurImage 2000;11:24–35
"... fMRI data are commonly analyzed by testing the time course from each voxel against specific hypothesized waveforms, despite the fact that many components of fMRI signals are difficult to specify explicitly. In contrast, purely datadriven techniques, by focusing on the intrinsic structure of the dat ..."
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Cited by 35 (3 self)
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fMRI data are commonly analyzed by testing the time course from each voxel against specific hypothesized waveforms, despite the fact that many components of fMRI signals are difficult to specify explicitly. In contrast, purely datadriven techniques, by focusing on the intrinsic structure of the data, lack a direct means to test hypotheses of interest to the examiner. Between these two extremes, there is a role for hybrid methods that use powerful datadriven techniques to fully characterize the data, but also use some a priori hypotheses to guide the analysis. Here we describe such a hybrid technique, HYBICA, which uses the initial characterization of the fMRI data from Independent Component Analysis and allows the experimenter to sequentially combine assumed taskrelated components so that one can gracefully navigate from a fully dataderived approach to a fully hypothesisdriven approach. We describe the results of testing the method with two artificial and two real data sets. A metric based on the diagnostic Predicted Sum of Squares statistic was used to select the best number of spatially independent components to combine and utilize in a standard regressional framework. The proposed metric provided an objective method to determine whether a more datadriven or a more hypothesisdriven approach was appropriate, depending on the degree of mismatch between the hypothesized reference function and the features in the data. HYBICA provides a robust way to combine the dataderived independent components into a dataderived activation waveform and suitable confounds so that standard statistical analysis can be performed. � 2000 Academic Press Key Words: linear regression; independent component analysis; data decomposition; functional magnetic resonance imaging
Comparison of two exploratory data analysis methods for fMRI: fuzzy clustering vs. principal component analysis
, 2000
"... Exploratory datadriven methods such as Fuzzy clustering analysis (FCA) and Principal component analysis (PCA) may be considered as hypothesisgenerating procedures that are complementary to the hypothesisled statistical inferential methods in functional magnetic resonance imaging (fMRI). Here, a c ..."
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Cited by 35 (2 self)
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Exploratory datadriven methods such as Fuzzy clustering analysis (FCA) and Principal component analysis (PCA) may be considered as hypothesisgenerating procedures that are complementary to the hypothesisled statistical inferential methods in functional magnetic resonance imaging (fMRI). Here, a comparison between FCA and PCA is presented in a systematic fMRI study, with MR data acquired under the null condition, i.e., no activation, with different noise contributions and simulated, varying "activation." The contrasttonoise (CNR) ratio ranged between 110. We found that if fMRI data are corrupted by scanner noise only, FCA and PCA show comparable performance. In the presence of other sources of signal variation (e.g., physiological noise), FCA outperforms PCA in the entire CNR range of interest in fMRI, particularly for low CNR values. The comparison method that we introduced may be used to assess other exploratory approaches such as independent component analysis or neural networkbased techniques. Crown Copyright # 2000. Published by Elsevier Science Inc.
The Statistical Analysis of fMRI Data
, 2008
"... In recent years there has been explosive growth in the number of neuroimaging studies performed using functional Magnetic Resonance Imaging (fMRI). The field that has grown around the acquisition and analysis of fMRI data is intrinsically interdisciplinary in nature and involves contributions from ..."
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Cited by 34 (0 self)
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In recent years there has been explosive growth in the number of neuroimaging studies performed using functional Magnetic Resonance Imaging (fMRI). The field that has grown around the acquisition and analysis of fMRI data is intrinsically interdisciplinary in nature and involves contributions from researchers in neuroscience, psychology, physics and statistics, among others. A standard fMRI study gives rise to massive amounts of noisy data with a complicated spatiotemporal correlation structure. Statistics plays a crucial role in understanding the nature of the data and obtaining relevant results that can be used and interpreted by neuroscientists. In this paper we discuss the analysis of fMRI data, from the initial acquisition of the raw data to its use in locating brain activity, making inference about brain connectivity and predictions about psychological or disease states. Along the way, we illustrate interesting and important issues where statistics already plays a crucial role. We also seek to illustrate areas where statistics has perhaps been underutilized and will have an increased role in the future.
Independent component analysis of biomedical signals
 In Proc. 2nd Int. Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000
, 2000
"... Biomedical signals from many sources including hearts, brains and endocrine systems pose a challenge to researchers who may have to separate weak signals arriving from multiple sources contaminated with artifacts and noise. The analysis of these signals is important both for research and for medical ..."
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Cited by 31 (3 self)
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Biomedical signals from many sources including hearts, brains and endocrine systems pose a challenge to researchers who may have to separate weak signals arriving from multiple sources contaminated with artifacts and noise. The analysis of these signals is important both for research and for medical diagnosis and treatment. The applications of Independent Component Analysis (ICA) to biomedical signals is a rapidly expanding area of research and many groups are now actively engaged in exploring the potential of blind signal separation and signal deconvolution for revealing new information about the brain and body. In this review, we survey some recent applications of ICA to a variety of electrical, magnetic and hemodynamic measurements, drawing primarily from our own research. 1.