A New Method for Spectral Decomposition Using a Bilinear Bayesian Approach

Ochs, Michael F.; Stoyanova, Radka; Arias‐Mendoza, Fernando; Brown, Truman R.

doi:10.1006/jmre.1998.1639

Cited by 92 publications

(52 citation statements)

References 19 publications

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“…A complete discussion on Bayesian approach to source separation can be found in [24][25][26]. However, its application to the case of positive sources and mixing has only received a few attention [27][28][29]. In this purpose, a recent contribution consists of the method termed by Bayesian positive source separation (BPSS) [2,30], which allows to jointly estimate source signals, mixing coefficients and regularization parameters in an unsupervised framework.…”

Section: Bayesian Positive Source Separationmentioning

confidence: 99%

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Moussaoui¹,

et al. 2008

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The surface of Mars is currently being imaged with an unprecedented combination of spectral and spatial resolution. This high resolution, and its spectral range, give the ability to pinpoint chemical species on the surface and the atmosphere of Mars moreaccurately than before. The subject of this paper is to present a method to extract informations on these chemicals from hyperspectral images. A first approach, based on Independent Component Analysis (ICA) [1], is able to extract artifacts and locations of CO2 and H2O ices. However, the main independence assumption and some basic properties (like the positivity of images and spectra) being unverified, the reliability of all the independent components (ICs) is weak. For improving the component extraction and consequently the endmember classification, a combination of spatial ICA with spectral Bayesian Positive Source Separation (BPSS) [2] is proposed. To reduce the computational burden, the basic idea is to use spatial ICA yielding a rough classification of pixels, which allows selection of small, but relevant, number of pixels and then BPSS is applied for the estimation of the source spectra using the spectral mixtures provided by this reduced set of pixels. Finally, the abundances of the components is assessed on the whole pixels of the images. Results of this approach are shown and evaluated by comparison with available reference spectra.

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Section: Bayesian Positive Source Separationmentioning

confidence: 99%

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Moussaoui¹,

et al. 2008

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“…Correspondence analysis ( (Abdi and Williams, 2010;Fellenberg et al, 2001) independent component analysis (ICA), (Hyvärinen et al, 2004;Kong et al, 2008;Lee and Batzoglou, 2003;Yao et al, 2012) , factor analysis (Abdi et al, 2013;Wouters et al, 2003) , canonical correlation analysis (CCA) (Lê Cao et al, 2009;Takane et al, 2008; , Laplacian eigenmaps, and spectral maps (Wouters et al, 2003) are related to the mathematics mainstays of singular value decomposition (SVD) (Eckart and Young, 1936) , and principal component analysis (PCA) (Hotelling, 1933;Ma and Dai, 2011;Pearson, 1901;Wall et al, 2003) based analysis. While, Non-negative Matrix Factorization (NMF) (Devarajan, 2008;Ochs and Fertig, 2012) , manifold learning (Maindonald, 2009;Moon et al, 2017) , and compressed sensing (Cleary et al, 2017;Vattikuti et al, 2014) draw on image processing methods (Lee and Seung, 1999;Ochs et al, 1999) . With the rapidly accelerating rate of high-throughput biological data acquisition, these MF techniques enable expanding beyond simple single study designs to power systems-level analyses.…”

Section: Overview Of Matrix Factorization In Genomicsmentioning

confidence: 99%

“…Therefore, learning gene modules in a manner that can account for a gene's participation in multiple pathways is critical to accurate biological interpretation. Non-negative matrix factorization (NMF) methods instead constrain all elements of the amplitude and pattern matrices to be greater than zero (Lee and Seung, 1999;Ochs et al, 1999) . This model has a twofold advantage.…”

Section: Data-driven Gene Sets From Mf Provide Context-dependent Corementioning

confidence: 99%

Enter the matrix: factorization uncovers knowledge from omics Names/Affiliations

Stein-O’Brien¹,

Arora

Culhane

et al. 2017

Preprint

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SummaryHigh-dimensional data is currently standard for biological inquiry. Biological systems are comprised of interrelated gene regulatory mechanisms, gene-gene interactions, and cellular interactions. These interactions induce low-dimensional structure within the high-dimensional data. Matrix factorization, also known as compressed sensing, learns low-dimensional mathematical representations from high-dimensional data. These factorization techniques can embed assumptions about pleiotropy, epistasis, inter-relationships between complex traits, and context-dependent interactions. They have been applied to uncover new biological knowledge in a breadth of topics ranging from pathway discovery to time course analysis. These techniques have been applied to data from diverse high-throughput omics technologies, including bulk and single-cell data. There are numerous computational techniques within the class of matrix factorization, each of which provides a unique interpretation of the processes in high-dimensional data. We review the visualization and applications of matrix factorization to systems-level analyses, which are diverse and require standardization to enable biological interpretation. Codifying the techniques to decipher biologically relevant features with matrix factorization enables their broad application to discovery beyond the limits of current biological knowledge-answering questions from high-dimensional data that we have not yet thought to ask.

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“…The formulation of source separation and factor analysis using Bayesian estimation theory has been suggested recently in [38][39][40][41] and used in signal and image processing problems. However, its application to the separation of spectral mixture data has only received a few attention [42][43][44]. Since only accounting for the non-negativity, mixture analysis still remains ill-posed, one has to use additional constraints or assumptions on the pure spectra and concentrations to get a unique solution.…”

Section: A Bayesian Approach To Spectral Mixture Analysismentioning

confidence: 99%

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Moussaoui

Carteret

Brie

et al. 2006

Chemometrics and Intelligent Laboratory Systems

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This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set.

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A New Method for Spectral Decomposition Using a Bilinear Bayesian Approach

Cited by 92 publications

References 19 publications

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

On the decomposition of Mars hyperspectral data by ICA and Bayesian positive source separation

Enter the matrix: factorization uncovers knowledge from omics Names/Affiliations

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

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