Nonnegative Matrix Factorization of Laboratory Astrophysical Ice Mixtures

Igual, Jorge; Llinares, Raul

doi:10.1109/jstsp.2008.2005324

Cited by 9 publications

(4 citation statements)

References 32 publications

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“…The primary aim of this paper is to explore the complexity of the bulge's MDF using GMM (Sect. 4.2-4.3), but in this section we describe an alternative decomposition using Non-negative Matrix Factorization (NMF; Lee & Seung 1999, with some examples of astrophysical applications in Igual &Llinares 2008 andHurley et al 2014). NMF is a dimensionality reduction technique similar to Principal Component Analysis (PCA) in spirit; one key difference is that the eigenvectors are constrained to be non-negative.…”

Section: Mdf Decomposition With Non-negative Matrix Factorizationmentioning

confidence: 99%

How Many Components? Quantifying the Complexity of the Metallicity Distribution in the Milky Way Bulge with APOGEE

Rojas-Arriagada,

Zasowski,

Schultheis

et al. 2020

Preprint

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We use data of ∼13.000 stars from the SDSS/APOGEE survey to study the shape of the MDF within the region |l| ≤ 11 • and |b| ≤ 13 • , and spatially constrained to R GC ≤ 3.5 kpc. We apply Gaussian Mixture Modeling (GMM) and Non-negative Matrix Factorization (NMF) decomposition techniques to identify the optimal number and the properties of MDF components in different spatial locations and under different sampling conditions. We find the shape and spatial variations of the MDF (at [Fe/H] ≥ −1 dex) are well represented as a smoothly varying contribution of three overlapping components located at [Fe/H] =+0.32, −0.17 and −0.66 dex. The bimodal MDF found in previous studies is in agreement with our trimodal assessment once the limitations in sample size and individual measurement errors are taken into account. The shape of the MDF and its correlations with kinematics reveal different spatial distributions and kinematical profiles for the three chemical components co-existing in the bulge region. We confirm the consensus physical interpretation of metal-rich stars as associated with the boxy/peanut X-shape bar, originating from the secular evolution of the early disc. On the other hand, metal-intermediate stars could be the product of in-situ formation at high redshift, in a gas-rich environment characterized by violent and fast star formation. This interpretation would help to link a present-day structure with those observed in formation in the center of high redshift galaxies. We refrain from associating the metal-poor stars with any particular formation mechanism. They seem to be inconsistent with being thick disc or halo stars, but may be the metal-rich tail of the population currently being characterized at lower metallicity from the study of RR Lyrae stars. Conversely, they could be associated with the metal-poor tail of the early thick disc.

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Section: Mdf Decomposition With Non-negative Matrix Factorizationmentioning

confidence: 99%

How Many Components? Quantifying the Complexity of the Metallicity Distribution in the Milky Way Bulge with APOGEE

Rojas-Arriagada,

Zasowski,

Schultheis

et al. 2020

Preprint

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“…The performance of these methods obtained on synthetic hyperspectral images and real data is promising. Future investigations include the analysis of algorithms such as those developed in [14][15][16] for estimating jointly the endmembers and abundances.…”

Section: Discussionmentioning

confidence: 99%

Linear unmixing of hyperspectral images using a scaled gradient method

Theys

Dobigeon

Tourneret

et al. 2009

2009 IEEE/SP 15th Workshop on Statistical Signal Processing

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This paper addresses the problem of linear unmixing for hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-toone and positivity constraints. Two scaled gradient iterative methods are proposed for estimating the abundances of the linear mixing model. The first method is obtained by including a normalization step in the scaled gradient method. The second method inspired by the fully constrained least squares algorithm includes the sum-to-one constraint in the observation model with an appropriate weighting parameter. Simulations on synthetic data illustrate the performance of these algorithms.

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“…NMF has been massively investigated because of the more interpretable results it provides when compared with methods without sign constraints. NMF was successfully applied to many fields, e.g., hyperspectral unmixing [5,6], astrophysics [7,8], fluorescence spectroscopy for agro-food analysis [9], audio signals [10], or environmental data processing [11].…”

Section: Introductionmentioning

confidence: 99%

Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

Delmaire

Omidvar

Puigt

et al. 2019

Entropy

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In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an α β -divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row sum-to-one property of one matrix factor. In this contribution, we extend our previous work which partly involved some of these aspects to α β -divergence cost functions. We derive new update rules which are extendthe previous ones and take into account the available information. Experiments conducted for several operating conditions on realistic simulated mixtures of particulate matter sources show the relevance of these approaches. Results from a real dataset campaign are also presented and validated with expert knowledge.

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Nonnegative Matrix Factorization of Laboratory Astrophysical Ice Mixtures

Cited by 9 publications

References 32 publications

How Many Components? Quantifying the Complexity of the Metallicity Distribution in the Milky Way Bulge with APOGEE

How Many Components? Quantifying the Complexity of the Metallicity Distribution in the Milky Way Bulge with APOGEE

Linear unmixing of hyperspectral images using a scaled gradient method

Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

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