Xi-Lin Li

University of Maryland, Baltimore County, Baltimore, Maryland, United States

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Publications (26)49.58 Total impact

  • Xi-Lin Li, T. Adali
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    ABSTRACT: We develop an efficient algorithm for noncircular complex independent component analysis (ICA) by optimizing the rows of separation matrix independently using a generalized Householder reflector and Newton method. We apply the new algorithm to the separation of complex generalized Gaussian distributed (GGD) sources, and propose a convenient way to learn the noncircularity of the sources. Simulation results are reported to study the convergence behavior, and confirm the superior performance of the new algorithm.
    IEEE Transactions on Signal Processing 01/2013; 61(24):6423-6430. · 2.81 Impact Factor
  • Xi-Lin Li, Tülay Adali
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    ABSTRACT: In this paper, we study the performance of mean square error (MSE) and Gaussian entropy criteria for linear and widely linear complex filtering. The MSE criterion has been extensively studied, and with a widely linear filter form, it can take into account the full second-order statistics of the input signal. However, it cannot exploit the full second-order statistics of the error, and doubles the dimension of the parameter vector to be estimated. In this paper, we introduce the use of Gaussian entropy criterion such that full second-order statistics of the error can be taken into account, and compare the performance of the Gaussian entropy and MSE criteria for a linear and widely linear filter implementation in batch and adaptive implementations. Detailed performance analysis with numerical examples is presented to investigate the relationship and performance differences of the two criteria in diverse scenarios.
    IEEE Transactions on Signal Processing 11/2012; 60(11):5672-5684. · 2.81 Impact Factor
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    ABSTRACT: We consider the problem of joint blind source separation of multiple datasets and introduce a solution to the problem for complex-valued sources. We pose the problem in an independent vector analysis (IVA) framework and provide a new general IVA implementation using Wirtinger calculus and a decoupled nonunitary optimization algorithm to facilitate Newton-based optimization. Utilizing the noncircular multivariate Gaussian distribution as a source prior enables the full utilization of the complete second-order statistics available in the covariance and pseudo-covariance matrices. The algorithm provides a principled approach for achieving multiset canonical correlation analysis.
    Signal Processing. 08/2012;
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    ABSTRACT: In this paper, we consider the joint blind source separation (JBSS) problem and introduce a number of algorithms to solve the JBSS problem using the independent vector analysis (IVA) framework. Source separation of multiple datasets simultaneously is possible when the sources within each and every dataset are independent of one another and each source is dependent on at most one source within each of the other datasets. In addition to source separation, the IVA framework solves an essential problem of JBSS, namely the identification of the dependent sources across the datasets. We propose to use the multivariate Gaussian source prior to achieve JBSS of sources that are linearly dependent across datasets. Analysis within the paper yields the local stability conditions, nonidentifiability conditions, and induced Cramér-Rao lower bound on the achievable interference to source ratio for IVA with multivariate Gaussian source priors. Additionally, by exploiting a novel nonorthogonal decoupling of the IVA cost function we introduce both Newton and quasi-Newton optimization algorithms for the general IVA framework.
    IEEE Transactions on Signal Processing 01/2012; 60(4):1672-1683. · 2.81 Impact Factor
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    ABSTRACT: Adaptive filtering has been extensively studied under the assumption that the noise is Gaussian. The most commonly used least-mean-square-error (LMSE) filter is optimal when the noise is Gaussian. However, in many practical applications, the noise can be modeled more accurately using a non-Gaussian distribution. In this correspondence, we consider non-Gaussian distributions for the noise model and show that the filter of using entropy bound minimization (EBM) leads to significant performance gain compared to the LMSE filter. The least mean p-norm (LMP) filter using the $\alpha$-stable distribution to model noise is shown to be the maximum-likelihood solution when using the generalized Gaussian distribution (GGD) to model noise. The GGD model for noise allows us to compute the Cramér–Rao lower bound (CRLB) for the error in estimating the weights. Simulations show that both the EBM and LMP filters achieve the CRLB as the sample size increases. The EBM filter is shown to be less committed with respect to unseen data yielding generally superior performance in online learning when compared to LMP. We also show that, when the noise comes from impulsive $\alpha$ -stable distributions, both the EBM and LMP filters provide better performance than LMSE. In addition, the EBM filter offers the advantage that it does not assume a certain parametric model for the noise, and by proper selection of the measuring functions, it can be adapted to a wide range of noise distributions.
    IEEE Transactions on Signal Processing 01/2012; 60(4):2049-2055. · 2.81 Impact Factor
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    ABSTRACT: Matrix optimization of cost functions is a common problem. Construction of methods that enable each row or column to be individually optimized, i.e., decoupled, are desirable for a number of reasons. With proper decoupling, the convergence characteristics such as local stability can be improved. Decoupling can enable density matching in applications such as independent component analysis (ICA). Lastly, efficient Newton algorithms become tractable after decoupling. The most common method for decoupling rows is to reduce the optimization space to orthogonal matrices. Such restrictions can degrade performance. We present a decoupling procedure that uses standard vector optimization procedures while still admitting nonorthogonal solutions. We utilize the decoupling procedure to develop a new decoupled ICA algorithm that uses Newton optimization enabling superior performance when the sample size is limited.
    Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on; 01/2012 · 4.63 Impact Factor
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    Xi-Lin Li, T. Adali, M. Anderson
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    ABSTRACT: One of the most commonly used data analysis tools, principal component analysis (PCA), since is based on variance maximization, assumes a circular model, and hence cannot account for the potential noncircularity of complex data. In this paper, we introduce noncircular PCA (ncPCA), which extends the traditional PCA to the case where there can be both circular and noncircular Gaussian signals in the subspace. We study the properties of ncPCA, introduce an efficient algorithm for its computation, and demonstrate its application to model selection, i.e., the detection of both the signal subspace order and the number of circular and noncircular signals. We present numerical results to demonstrate the advantages of ncPCA over regular PCA when there are noncircular signals in the subspace. At the same time, we note that since a noncircular model has more degrees of freedom than a circular one, there are cases where a circular model might be preferred even though the underlying problem is noncircular. In particular, we show that a circular model is preferred when the signal-to-noise ratio (SNR) is low, number of samples is small, or the degree of noncircularity of the signals is low. Hence, ncPCA inherently provides guidance as to when to take noncircularity into account.
    IEEE Transactions on Signal Processing 11/2011; · 2.81 Impact Factor
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    ABSTRACT: In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.
    IEEE transactions on bio-medical engineering 09/2011; 58(12):3406-17. · 2.15 Impact Factor
  • Xi-Lin Li, T. Adali
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    ABSTRACT: We introduce a new blind source separation (BSS) algorithm for correlated noncircular sources that uses only second-order statistics and fully takes the correlation structure into account. We propose a parametric entropy rate estimator that uses a widely linear autoregressive (AR) model for the sources, and derive the BSS algorithm by minimizing the mutual information of separated time series. We compare the performance of the new algorithm with competing algorithms and demonstrate its superior separation performance as well as its effectiveness in separation of non-Gaussian sources when the identification conditions are met.
    IEEE Transactions on Signal Processing 07/2011; · 2.81 Impact Factor
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    ABSTRACT: Independent component analysis (ICA) has proven useful for the analysis of functional magnetic resonance imaging (fMRI) data. In this paper, we compare the performance of three ICA algorithms and show the importance of taking sample correlation information into account. The three ICA algorithms are Infomax, the most widely used algorithm for fMRI analysis, entropy bound minimization (EBM) that adapts to a wide range of source distributions, and full blind source separation (FBSS) which has the ability to incorporate a flexible density model along with sample correlation information. We apply these three ICA algorithms to fMRI data from multiple subjects performing an auditory oddball task (AOD). We show that FBSS leads to significant improvement in the estimation of both the spatial activation and the time courses of several components. More importantly, by taking the correlation information into account, the default mode network (DMN) component, an important one in the study of brain function, is more consistently estimated using FBSS.
    Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on; 05/2011
  • Xi-Lin Li, T. Adali
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    ABSTRACT: In this paper, we study the performance of mean square error (MSE) and Gaussian entropy criteria for linear and widely linear complex filtering. The MSE criterion cannot exploit the full second-order statistics of the error signal. To this end, we propose a new Gaussian entropy criterion to exploit the full second-order statistics of the error signal, and compare the performance of the two criteria in linear and widely linear filters. We show that the minimum Gaussian entropy estimator is also the best linear unbiased estimator (BLUE).
    Information Sciences and Systems (CISS), 2011 45th Annual Conference on; 04/2011
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    ABSTRACT: In independent component analysis (ICA) of func- tional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order seg- mentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence—mutual information—among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modu- lation of the spatial maps, i.e., temporal information, our ICA- based approach incorporates both spatial and temporal informa- tion effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain net- works, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components re- lated to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distin- guished from other components of interest.
    IEEE Transactions on Biomedical Engineering 01/2011; 58:3406-3417. · 2.35 Impact Factor
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    ABSTRACT: In this paper, we show that the joint blind source separation (JBSS) problem can be solved by jointly diagonalizing cumulant matrices of any order higher than one, including the correlation matrices and the fourth-order cumulant matrices. We introduce an efficient iterative generalized joint diagonalization algorithm such that a series of orthogonal procrustes problems are solved. We present simulation results to show that the new algorithms can reliably solve the permutation ambiguity in JBSS and that they offer superior performance compared with existing multiset canonical correlation analysis (MCCA) and independent vector analysis (IVA) approaches. Experiment on real-world data for separation of fetal heartbeat in electrocardiogram (ECG) data demonstrates a new application of JBSS, and the success of the new algorithms for a real-world problem.
    Signal Processing. 01/2011; 91:2314-2322.
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    ABSTRACT: Estimation of the order of functional magnetic resonance imaging (fMRI) data is a crucial step in data-driven methods assuming a multivariate linear model. Use of information theoretic criteria for model order detection was proven useful but the sample dependence in fMRI data limits this usefulness. In this paper, we propose an iterative procedure that jointly estimates the downsampling depth and order of fMRI data, both by using information theoretic criteria. Experimental results on real-world fMRI data show reliable performance of the new method. Order analysis on auditory oddball task (AOD) data of healthy and schizophrenia subjects suggests that model order can be a promising biomarker for mental disorders.
    Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2011, March 30 - April 2, 2011, Chicago, Illinois, USA; 01/2011
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    ABSTRACT: This paper presents a novel algorithm for independent vector analysis (IVA) of Gaussian data sets. Following a maximum likelihood (ML) approach, we show that the cost function to be minimized by the proposed GML-IVA algorithm reduces to an estimate of the mutual information among the different sets of latent variables. The proposed method, which can be seen as a new generalization of canonical correlation analysis (CCA), is based on the sequential solution of different least squares problems obtained from the quadratic approximation of the non-convex IVA cost function. The convergence and performance of the proposed algorithm are illustrated by means of several simulation examples, including an application consisting in the joint blind source separation (J-BSS) of three color images.
    01/2011;
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    ABSTRACT: This paper considers the problem of joint blind source separation (J-BSS), which appears in many practical problems such as blind deconvolution or functional magnetic resonance imaging (fMRI). In particular, we establish the necessary and sufficient conditions for the solution of the J-BSS problem by exclusively exploiting the second-order statistics (SOS) of the observations. The identifiability analysis is based on the idea of equivalently distributed sets of latent variables, that is, latent variables with covariance matrices related by means of a diagonal matrix. Interestingly, the identifiability analysis also allows us to introduce a measure of the identifiability degree based on Kullback-Leibler projections. This measure is clearly correlated with the performance of practical SOS-based J-BSS algorithms, which is illustrated by means of numerical examples.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011 · 4.63 Impact Factor
  • Xi-Lin Li, M. Anderson, T. Adali
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    ABSTRACT: The commonly used principal component analysis (PCA) assumes circular Gaussian distribution for the observed complex random variables. This paper extends PCA to the general case where the signals can be noncircular, and introduces a new PCA method called the noncircular PCA (ncPCA). We study the properties of ncPCA and propose an efficient algorithm for its implementation. Numerical results are presented to demonstrate its advantages in signal detection and subspace estimation, in particular when the circularity assumptions on data do not hold.
    Signals, Systems and Computers (ASILOMAR), 2010 Conference Record of the Forty Fourth Asilomar Conference on; 12/2010
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    Xi-Lin Li, T. Adali
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    ABSTRACT: A novel (differential) entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations, and is computed using a numerical procedure thus resulting in accurate estimates for the entropy. We show that such an estimator exists for a wide class of measuring functions, and provide a number of design examples to demonstrate its flexible nature. We then derive a novel independent component analysis (ICA) algorithm that uses the entropy estimate thus obtained, ICA by entropy bound minimization (ICA-EBM). The algorithm adopts a line search procedure, and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance. We demonstrate the superior performance of ICA-EBM and its ability to match sources that come from a wide range of distributions using simulated and real-world data.
    IEEE Transactions on Signal Processing 11/2010; · 2.81 Impact Factor
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    Xi-Lin Li, T. Adali
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    ABSTRACT: We first present a new (differential) entropy estimator for complex random variables by approximating the entropy estimate using a numerically computed maximum entropy bound. The associated maximum entropy distributions belong to the class of weighted linear combinations and elliptical distributions, and together, they provide a rich array of bivariate distributions for density matching. Next, we introduce a new complex independent component analysis (ICA) algorithm, complex ICA by entropy-bound minimization (complex ICA-EBM), using this new entropy estimator and a line search optimization procedure. We present simulation results to demonstrate the superior separation performance and computational efficiency of complex ICA-EBM in separation of complex sources that come from a wide range of bivariate distributions.
    Circuits and Systems I: Regular Papers, IEEE Transactions on 08/2010; · 2.24 Impact Factor
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    Xi-Lin Li, T. Adali
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    ABSTRACT: We propose a new entropy rate estimator for a second and/or higher-order correlated source by modeling it as the output of a linear filter, which can be mixed-phase, driven by Gaussian or non-Gaussian noise. Based on this estimator, we develop a new spatiotemporal blind source separation (BSS) algorithm, full BSS (FBSS), by minimizing the entropy rate of separated sources. FBSS provides more flexibilities in exploiting the temporal structures of sources than the state-of-the-art spatiotemporal BSS algorithms, which use AR models, and thus imply minimum-phase property of sources.
    Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor