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Nonnegative matrix factorization with Gaussian process priors.

Schmidt MN, Laurberg H - Comput Intell Neurosci (2008)

Bottom Line: We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors.We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function.This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries.

View Article: PubMed Central - PubMed

Affiliation: Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, DTU-Building 321, 2800 Lyngby, Denmark. mns@imm.dtu.dk

ABSTRACT
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging.

No MeSH data available.


Brain imagingdata matrix (top) along with the estimated decomposition and residual for theCNMF (middle) and GPP-NMF (bottom) methods. In this view, the results of the twodecompositions are very similar, the data appears to be modeled equally welland the residuals are similar in magnitude.
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fig4: Brain imagingdata matrix (top) along with the estimated decomposition and residual for theCNMF (middle) and GPP-NMF (bottom) methods. In this view, the results of the twodecompositions are very similar, the data appears to be modeled equally welland the residuals are similar in magnitude.

Mentions: Next, wedemonstrate the GPP-NMF method on 1H decoupled 31P chemical shift imaging data of the human brain. We use the data setfrom Ochs et al. [24],which has also been analyzed by Sajda et al. [6, 7]. The data set, which isshown in Figure 4, consists of 512 spectra measured on an 8 × 8 × 8 grid in the brain.


Nonnegative matrix factorization with Gaussian process priors.

Schmidt MN, Laurberg H - Comput Intell Neurosci (2008)

Brain imagingdata matrix (top) along with the estimated decomposition and residual for theCNMF (middle) and GPP-NMF (bottom) methods. In this view, the results of the twodecompositions are very similar, the data appears to be modeled equally welland the residuals are similar in magnitude.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2367383&req=5

fig4: Brain imagingdata matrix (top) along with the estimated decomposition and residual for theCNMF (middle) and GPP-NMF (bottom) methods. In this view, the results of the twodecompositions are very similar, the data appears to be modeled equally welland the residuals are similar in magnitude.
Mentions: Next, wedemonstrate the GPP-NMF method on 1H decoupled 31P chemical shift imaging data of the human brain. We use the data setfrom Ochs et al. [24],which has also been analyzed by Sajda et al. [6, 7]. The data set, which isshown in Figure 4, consists of 512 spectra measured on an 8 × 8 × 8 grid in the brain.

Bottom Line: We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors.We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function.This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries.

View Article: PubMed Central - PubMed

Affiliation: Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, DTU-Building 321, 2800 Lyngby, Denmark. mns@imm.dtu.dk

ABSTRACT
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging.

No MeSH data available.