Exploring multimodal data fusion through joint decompositions with flexible couplings

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.Comment: 15 pages, 7 figures, revised versio

Early soft and flexible fusion of electroencephalography and functional magnetic resonance imaging via double coupled matrix tensor factorization for multisubject group analysis

Data fusion refers to the joint analysis of multiple datasets that provide different (e.g., complementary) views of the same task. In general, it can extract more information than separate analyses can. Jointly analyzing electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measurements has been proved to be highly beneficial to the study of the brain function, mainly because these neuroimaging modalities have complementary spatiotemporal resolution: EEG offers good temporal resolution while fMRI is better in its spatial resolution. The EEG–fMRI fusion methods that have been reported so far ignore the underlying multiway nature of the data in at least one of the modalities and/or rely on very strong assumptions concerning the relation of the respective datasets. For example, in multisubject analysis, it is commonly assumed that the hemodynamic response function is a priori known for all subjects and/or the coupling across corresponding modes is assumed to be exact (hard). In this article, these two limitations are overcome by adopting tensor models for both modalities and by following soft and flexible coupling approaches to implement the multimodal fusion. The obtained results are compared against those of parallel independent component analysis and hard coupling alternatives, with both synthetic and real data (epilepsy and visual oddball paradigm). Our results demonstrate the clear advantage of using soft and flexible coupled tensor decompositions in scenarios that do not conform with the hard coupling assumption

Performance bounds for coupled models

Two models are called "coupled" when a non empty set of the underlying parameters are related through a differentiable implicit function. The goal is to estimate the parameters of both models by merging all datasets, that is, by processing them jointly. In this context, we show that the parameter estimation accuracy under a general class of dataset distributions always improves when compared to an equivalent uncoupled model. We eventually illustrate our results with the fusion of multiple tensor data

Joint Tensor Compression for Coupled Canonical Polyadic Decompositions

International audienceTo deal with large multimodal datasets, coupled canonical polyadic decompositions are used as an approximation model. In this paper, a joint compression scheme is introduced to reduce the dimensions of the dataset. Joint compression allows to solve the approximation problem in a compressed domain using standard coupled decomposition algorithms. Computational complexity required to obtain the coupled decomposition is therefore reduced. Also, we propose to approximate the update of the coupled factor by a simple weighted average of the independent updates of the coupled factors. The proposed approach and its simplified version are tested with synthetic data and we show that both do not incur substantial loss in approximation performance

A Tour of Constrained Tensor Canonical Polyadic Decomposition

This paper surveys the use of constraints in tensor decomposition models. Constrained tensor decompositions have been extensively applied to chemometrics and array processing, but there is a growing interest in understanding these methods independently of the application of interest. We suggest a formalism that unifies various instances of constrained tensor decomposition, while shedding light on some possible extensions of existing methods

Coupled CP tensor decomposition with shared and distinct components for multi-task fMRI data fusion

Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data. Coupled matrix and tensor factorization approaches have been useful for flexible data fusion, or decomposition to extract features that can be used in multiple ways. However, existing methods do not directly recover shared and dataset-specific components, which requires post-processing steps involving additional hyperparameter selection. In this paper, we propose a tensor-based framework for multi-task fMRI data fusion, using a partially constrained canonical polyadic (CP) decomposition model. Differently from previous approaches, the proposed method directly recovers shared and dataset-specific components, leading to results that are directly interpretable. A strategy to select a highly reproducible solution to the decomposition is also proposed. We evaluate the proposed methodology on real fMRI data of three tasks, and show that the proposed method finds meaningful components that clearly identify group differences between patients with schizophrenia and healthy controls

Exploring coupled images fusion based on joint tensor decomposition

Data fusion has always been a hot research topic in human-centric computing and extended with the development of artificial intelligence. Generally, the coupled data fusion algorithm usually utilizes the information from one data set to improve the estimation accuracy and explain related latent variables of other coupled datasets. This paper proposes several kinds of coupled images decomposition algorithms based on the coupled matrix and tensor factorization-optimization (CMTF-OPT) algorithm and the flexible coupling algorithm, which are termed the coupled images factorization-optimization(CIF-OPT) algorithm and the modified flexible coupling algorithm respectively. The theory and experiments show that the effect of the CIF-OPT algorithm is robust under the influence of different noises. Particularly, the CIF-OPT algorithm can accurately restore an image with missing some data elements. Moreover, the flexible coupling model has better estimation performance than a hard coupling. For high-dimensional images, this paper adopts the compressed data decomposition algorithm that not only works better than uncoupled ALS algorithm as the image noise level increases, but saves time and cost compared to the uncompressed algorithm

Unraveling Diagnostic Biomarkers of Schizophrenia Through Structure-Revealing Fusion of Multi-Modal Neuroimaging Data

Fusing complementary information from different modalities can lead to the discovery of more accurate diagnostic biomarkers for psychiatric disorders. However, biomarker discovery through data fusion is challenging since it requires extracting interpretable and reproducible patterns from data sets, consisting of shared/unshared patterns and of different orders. For example, multi-channel electroencephalography (EEG) signals from multiple subjects can be represented as a third-order tensor with modes: subject, time, and channel, while functional magnetic resonance imaging (fMRI) data may be in the form of subject by voxel matrices. Traditional data fusion methods rearrange higher-order tensors, such as EEG, as matrices to use matrix factorization-based approaches. In contrast, fusion methods based on coupled matrix and tensor factorizations (CMTF) exploit the potential multi-way structure of higher-order tensors. The CMTF approach has been shown to capture underlying patterns more accurately without imposing strong constraints on the latent neural patterns, i.e., biomarkers. In this paper, EEG, fMRI, and structural MRI (sMRI) data collected during an auditory oddball task (AOD) from a group of subjects consisting of patients with schizophrenia and healthy controls, are arranged as matrices and higher-order tensors coupled along the subject mode, and jointly analyzed using structure-revealing CMTF methods [also known as advanced CMTF (ACMTF)] focusing on unique identification of underlying patterns in the presence of shared/unshared patterns. We demonstrate that joint analysis of the EEG tensor and fMRI matrix using ACMTF reveals significant and biologically meaningful components in terms of differentiating between patients with schizophrenia and healthy controls while also providing spatial patterns with high resolution and improving the clustering performance compared to the analysis of only the EEG tensor. We also show that these patterns are reproducible, and study reproducibility for different model parameters. In comparison to the joint independent component analysis (jICA) data fusion approach, ACMTF provides easier interpretation of EEG data by revealing a single summary map of the topography for each component. Furthermore, fusion of sMRI data with EEG and fMRI through an ACMTF model provides structural patterns; however, we also show that when fusing data sets from multiple modalities, hence of very different nature, preprocessing plays a crucial role

Dictionary-based Tensor Canonical Polyadic Decomposition

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images