Exploring multimodal data fusion through joint decompositions with flexible couplings
arXiv:1505.07717 · doi:10.1109/TSP.2016.2576425
Abstract
A Bayesian framework is proposed to define flexible coupling models for joint tensor decompositions of multiple data sets. Under this framework, a natural formulation of the data fusion problem is to cast it in terms of a joint maximum a posteriori (MAP) estimator. Data driven scenarios of joint posterior distributions are provided, including general Gaussian priors and non Gaussian coupling priors. We present and discuss implementation issues of algorithms used to obtain the joint MAP estimator. We also show how this framework can be adapted to tackle the problem of joint decompositions of large datasets. In the case of a conditional Gaussian coupling with a linear transformation, we give theoretical bounds on the data fusion performance using the Bayesian Cramer-Rao bound. Simulations are reported for hybrid coupling models ranging from simple additive Gaussian models, to Gamma-type models with positive variables and to the coupling of data sets which are inherently of different size due to different resolution of the measurement devices.
15 pages, 7 figures, revised version
References in corpus (2)
Cited by in corpus (9)
- Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach
- Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation
- A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings
- Dictionary-based Tensor Canonical Polyadic Decomposition
- Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms
- Early soft and flexible fusion of EEG and fMRI via tensor decompositions
- Coupled CP tensor decomposition with shared and distinct components for multi-task fMRI data fusion
- PARAFAC2-based Coupled Matrix and Tensor Factorizations with Constraints
- A Coupled Random Projection Approach to Large-Scale Canonical Polyadic Decomposition