Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems

Benthem, Mark Hilary Van; Keenan, Michael R.

doi:10.1002/cem.889

Cited by 212 publications

(160 citation statements)

References 9 publications

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“…Spectral image data were combined into a composite image and analyzed with in-house-written MCR algorithms (Bro and De Jong, 1997;Van Benthem et al, 2002;Haaland et al, 2003;Keenan and Kotula, 2004;Baker, 2008) and software Haaland et al, 2009). MCR is an iterative numerical analysis method implemented using constrained alternating least squares (Van Benthem and Keenan, 2004) and generates spectral components that combine in a linear additive manner to recreate noise-free spectroscopic data. The MCR model is applied to the spectral images on a per pixel basis to generate concentration maps that give the relative concentration and location of spectral components within the image.…”

Section: Data Processingmentioning

confidence: 99%

Photosynthetic Pigment Localization and Thylakoid Membrane Morphology Are Altered in Synechocystis 6803 Phycobilisome Mutants

et al. 2012

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(M.L., H.B.P.) Cyanobacteria are oxygenic photosynthetic prokaryotes that are the progenitors of the chloroplasts of algae and plants. These organisms harvest light using large membrane-extrinsic phycobilisome antenna in addition to membrane-bound chlorophyllcontaining proteins. Similar to eukaryotic photosynthetic organisms, cyanobacteria possess thylakoid membranes that house photosystem (PS) I and PSII, which drive the oxidation of water and the reduction of NADP + , respectively. While thylakoid morphology has been studied in some strains of cyanobacteria, the global distribution of PSI and PSII within the thylakoid membrane and the corresponding location of the light-harvesting phycobilisomes are not known in detail, and such information is required to understand the functioning of cyanobacterial photosynthesis on a larger scale. Here, we have addressed this question using a combination of electron microscopy and hyperspectral confocal fluorescence microscopy in wild-type Synechocystis species PCC 6803 and a series of mutants in which phycobilisomes are progressively truncated. We show that as the phycobilisome antenna is diminished, large-scale changes in thylakoid morphology are observed, accompanied by increased physical segregation of the two photosystems. Finally, we quantified the emission intensities originating from the two photosystems in vivo on a per cell basis to show that the PSI:PSII ratio is progressively decreased in the mutants. This results from both an increase in the amount of photosystem II and a decrease in the photosystem I concentration. We propose that these changes are an adaptive strategy that allows cells to balance the light absorption capabilities of photosystems I and II under light-limiting conditions.

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Section: Data Processingmentioning

confidence: 99%

Photosynthetic Pigment Localization and Thylakoid Membrane Morphology Are Altered in Synechocystis 6803 Phycobilisome Mutants

et al. 2012

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“…The nnls function solves the nonnegativity-constrained least squares problem. For this work we used a simple modification of a published procedure [37] that allows matrix cross-products to be input rather than computing them in the first step of the algorithm. A fixed number of alternating least-squares iterations, 500, was used to compute the results presented here.…”

Section: Appendix: Matlab-like Pseudocode For the Mcr-als Calculationsmentioning

confidence: 99%

Exploiting spatial‐domain simplicity in spectral image analysis

Keenan

2009

Surface & Interface Analysis

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Full-spectrum imaging is fast becoming a tool of choice for characterizing heterogeneous materials. Spectral images, which consist of a complete spectrum at each point in a spatial array, can be acquired from a wide variety of surface and microanalytical spectroscopic techniques. It is not uncommon that such spectral image data sets comprise tens of thousands of individual spectra, or more. Given the vast quantities of raw spectral data, factor analysis methods have proved indispensable for extracting the chemical information from these high-dimensional data sets into a limited number of factors that represent the spectral and spatial characteristics of the sample's composition. It is well known that factor models suffer a 'rotational ambiguity', that is, there are an infinite number of factor models that will fit the data equally well. Thus, physically inspired constraints are often employed to derive relatively unique models that make the individual factors more easily interpreted by the practicing analyst. In the present work, we note that many samples undergoing spectral image analysis are 'simple' in the sense that only one or a few of the sample's constituents are present at any particular location. When this situation prevails, simplicity in the spatial domain can be exploited to make the resulting factor models more realistic. In particular, orthogonal rotation of the spatial-domain vectors arising from singular value decomposition (SVD) of the spectral data matrix will be shown to be an effective method for making physically acceptable and easily interpretable estimates of the pure-component spectra and abundances.

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“…A classical method for solving the NNLS problem is the active set method of Lawson and Hanson [20]; however, applying Lawson and Hanson's method directly to NNCP is extremely slow. Bro and De Jong [4] suggested an improved active-set method to solve the NNLS problems, and Ven Benthem and Keenan [28] further accelerated the active-set method, which was later utilized in NMF [14] and NNCP [15]. In Friedlander and Hatz [10], the NNCP subproblems are solved by a two-metric projected gradient descent method.…”

Section: Related Workmentioning

confidence: 99%

Fast Nonnegative Tensor Factorization with an Active-Set-Like Method

Kim

Park

2012

High-Performance Scientific Computing

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We introduce an efficient algorithm for computing a low-rank nonnegative CANDECOMP/PARAFAC (NNCP) decomposition. In text mining, signal processing, and computer vision among other areas, imposing nonnegativity constraints to the low-rank factors of matrices and tensors has been shown an effective technique providing physically meaningful interpretation. A principled methodology for computing NNCP is alternating nonnegative least squares, in which the nonnegativity-constrained least squares (NNLS) problems are solved in each iteration. In this chapter, we propose to solve the NNLS problems using the block principal pivoting method. The block principal pivoting method overcomes some difficulties of the classical active method for the NNLS problems with a large number of variables. We introduce techniques to accelerate the block principal pivoting method for multiple right-hand sides, which is typical in NNCP computation. Computational experiments show the state-of-the-art performance of the proposed method.

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Fast algorithm for the solution of large‐scale non‐negativity‐constrained least squares problems

Cited by 212 publications

References 9 publications

Photosynthetic Pigment Localization and Thylakoid Membrane Morphology Are Altered in Synechocystis 6803 Phycobilisome Mutants

Photosynthetic Pigment Localization and Thylakoid Membrane Morphology Are Altered in Synechocystis 6803 Phycobilisome Mutants

Exploiting spatial‐domain simplicity in spectral image analysis

Fast Nonnegative Tensor Factorization with an Active-Set-Like Method

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