Abstract
A Bayesian framework is proposed to define flexible coupling models for joint decompositions of data sets. Under this framework, a solution to the joint decomposition can be cast in terms of a maximum a posteriori estimator. Examples of joint posterior distributions are provided, including general Gaussian priors and non Gaussian coupling priors. Then simulations are reported and show the effectiveness of this approach to fuse information from data sets, which are inherently of different size due to different time resolution of the measurement devices.
R.C. Farias—This research was supported in part by the ERC Grants AdG-2013-320594 “DECODA” (R. Cabral Farias, J. E. Cohen and P. Comon) and AdG-2012-320684 “CHESS” (Christian Jutten). This paper is a short version of a report available online at: https://hal.archives-ouvertes.fr/hal-01135920/.
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Notes
- 1.
We could also consider a minimum mean squared error setting but then we would need to evaluate \(p(\varvec{\mathcal {Y}},\varvec{\mathcal {Y}}')\), which is normally cumbersome.
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Cabral Farias, R., Cohen, J.E., Jutten, C., Comon, P. (2015). Joint Decompositions with Flexible Couplings. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_14
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