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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.


GPP-NMFdecomposition result. The recovered spectra are very similar to the spectrafound by the CNMF method, but they are slightly more smooth. The spatialdistribution in the brain is highly separated between brain and muscle tissue,and it is more symmetric than the CNMF solution.
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fig7: GPP-NMFdecomposition result. The recovered spectra are very similar to the spectrafound by the CNMF method, but they are slightly more smooth. The spatialdistribution in the brain is highly separated between brain and muscle tissue,and it is more symmetric than the CNMF solution.

Mentions: We then decomposed the data set using the proposedGPP-NMF algorithm and, for comparison, reproduced the results of Sajda et al.[7] using their CNMFmethod. The results of the experiments are shown in Figure 4. An example of arandom draw from the prior distribution is shown in Figure 5. The results ofthe CNMF is shown in Figure 6, and the results of the GPP-NMF is shown inFigure 7. The figures show the constituent spectra and the fifth axial slice ofthe spatial distribution of the spectra. The 8 × 8 spatial distributions are smoothed in theillustration, similar to the way the results are visualized in the literature.


Nonnegative matrix factorization with Gaussian process priors.

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

GPP-NMFdecomposition result. The recovered spectra are very similar to the spectrafound by the CNMF method, but they are slightly more smooth. The spatialdistribution in the brain is highly separated between brain and muscle tissue,and it is more symmetric than the CNMF solution.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2367383&req=5

fig7: GPP-NMFdecomposition result. The recovered spectra are very similar to the spectrafound by the CNMF method, but they are slightly more smooth. The spatialdistribution in the brain is highly separated between brain and muscle tissue,and it is more symmetric than the CNMF solution.
Mentions: We then decomposed the data set using the proposedGPP-NMF algorithm and, for comparison, reproduced the results of Sajda et al.[7] using their CNMFmethod. The results of the experiments are shown in Figure 4. An example of arandom draw from the prior distribution is shown in Figure 5. The results ofthe CNMF is shown in Figure 6, and the results of the GPP-NMF is shown inFigure 7. The figures show the constituent spectra and the fifth axial slice ofthe spatial distribution of the spectra. The 8 × 8 spatial distributions are smoothed in theillustration, similar to the way the results are visualized in the literature.

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.