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Nonnegative matrix factorization with sparseness constraints
 Jour. of
, 2004
"... www.cs.helsinki.fi/patrik.hoyer ..."
Nonnegative sparse coding, in
 Proc. IEEE Workshop on Neural Networks for Signal Processing (NNSP’2002), 2002
"... Abstract. Nonnegative sparse coding is a method for decomposing multivariate data into nonnegative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and nonnegative matrix factorization. We then gi ..."
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Cited by 167 (3 self)
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Abstract. Nonnegative sparse coding is a method for decomposing multivariate data into nonnegative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and nonnegative matrix factorization. We then give a simple yet efficient multiplicative algorithm for finding the optimal values of the hidden components. In addition, we show how the basis vectors can be learned from the observed data. Simulations demonstrate the effectiveness of the proposed method.
Hyperspectral unmixing overview: Geometrical, statistical, and sparse regressionbased approaches
 IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens
, 2012
"... Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). H ..."
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Cited by 104 (34 self)
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Abstract—Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, illposed
Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery
"... Abstract—This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown e ..."
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Cited by 76 (36 self)
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Abstract—This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and fulladditivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images. Index Terms—Bayesian inference, endmember extraction, hyperspectral imagery, linear spectral unmixing, MCMC methods. I.
Does independent component analysis play a role in unmixing hyperspectral data
 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
, 2005
"... Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2) ..."
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Cited by 61 (12 self)
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Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2) sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signaltonoise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.
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.
A ‘nonnegative PCA’ algorithm for independent component analysis, 2002, submitted for publication
"... We consider the task of independent component analysis when the independent sources are known to be nonnegative and wellgrounded, so that they have a nonzero probability density function (pdf) in the region of zero. We propose the use of a "nonnegative principal component analysis (nonnegative ..."
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Cited by 37 (3 self)
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We consider the task of independent component analysis when the independent sources are known to be nonnegative and wellgrounded, so that they have a nonzero probability density function (pdf) in the region of zero. We propose the use of a "nonnegative principal component analysis (nonnegative PCA) " algorithm, which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and we conjecture that this algorithm will find such nonnegative wellgrounded independent sources, under reasonable initial conditions. While the algorithm has proved difficult to analyze in the general case, we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation. Index Terms independent component analysis learning (artificial intelligence) matrix decomposition principal component analysis independent component analysis nonlinear principal component analysis nonnegative PCA algorithm nonnegative matrix factorization nonzero probability density function rectification nonlinearity subspace learning rule ©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any
Resampling approach to estimate the stability of onedimensional or multidimensional independent components
 IEEE Transactions on Biomedical Engineering
, 2002
"... AbstractWhen applying unsupervised learning techniques in biomedical data analysis, a key question is whether the estimated parameters of the studied system are reliable. In other words, can we assess the quality of the result produced by our learning technique? We propose resampling methods to tac ..."
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Cited by 29 (5 self)
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AbstractWhen applying unsupervised learning techniques in biomedical data analysis, a key question is whether the estimated parameters of the studied system are reliable. In other words, can we assess the quality of the result produced by our learning technique? We propose resampling methods to tackle this question and illustrate their usefulness for Blind Source Separation (BSS). We demonstrate that our proposed reliability estimation can be used to discover stable one or multidimensional independent components, to choose the appropriate BSSmodel, to enhance signicantly the separation performance, and, most important, to
ag components that carry physical meaning. Application to dierent biomedical testbed data sets (MEG/ECGrecordings) underline the usefulness of our approach. KeywordsBlind Source Separation, bootstrap, electrocardiography (ECG), independent component analysis (ICA), magnetoencephalography (MEG), multidimensional ICA, reliability, resampling, stability, unsupervised learning I.