Limits...
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: random draw from the prior distribution with the parameters set asdescribed in the text. The prior distribution of the constituent spectra (left)is exponential and smooth, and the spatial distribution (right) in the brain isexponential, smooth, and has a left-to-right symmetry.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2367383&req=5

fig5: Brain imagingdata: random draw from the prior distribution with the parameters set asdescribed in the text. The prior distribution of the constituent spectra (left)is exponential and smooth, and the spatial distribution (right) in the brain isexponential, smooth, and has a left-to-right symmetry.

Mentions: The GPP-NMF approach we propose in this paper bridgesthe gap between the two previous approaches, in the sense that it is arelatively fast NMF approach, in which priors over the factors can bespecified. These priors are specified by the choice of the link and covariancefunctions. We used prior predictive sampling to find reasonable settings of thethe function parameters: we drew random samples from the prior distribution andexamined properties of the factors and reconstructed data. We then manuallyadjusted the parameters of the prior to match our prior beliefs. An example ofa random draw from the prior distribution is shown in Figure 5, with theparameters set as described below.


Nonnegative matrix factorization with Gaussian process priors.

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

Brain imagingdata: random draw from the prior distribution with the parameters set asdescribed in the text. The prior distribution of the constituent spectra (left)is exponential and smooth, and the spatial distribution (right) in the brain isexponential, smooth, and has a left-to-right symmetry.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig5: Brain imagingdata: random draw from the prior distribution with the parameters set asdescribed in the text. The prior distribution of the constituent spectra (left)is exponential and smooth, and the spatial distribution (right) in the brain isexponential, smooth, and has a left-to-right symmetry.
Mentions: The GPP-NMF approach we propose in this paper bridgesthe gap between the two previous approaches, in the sense that it is arelatively fast NMF approach, in which priors over the factors can bespecified. These priors are specified by the choice of the link and covariancefunctions. We used prior predictive sampling to find reasonable settings of thethe function parameters: we drew random samples from the prior distribution andexamined properties of the factors and reconstructed data. We then manuallyadjusted the parameters of the prior to match our prior beliefs. An example ofa random draw from the prior distribution is shown in Figure 5, with theparameters set as described below.

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.