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.

Joint blind source separation (JBSS) is a powerful tool for analyzing multiple linked datasets, distinguished by the key ability to exploit cross-dataset dependencies. Despite this ability generally improving overall estimation performance, joint decompositions also incur considerable computational costs, which can lead to intractable problems with hundreds or thousands of datasets. In this paper, we introduce an efficient method for large-scale JBSS by multilinear regression. We consider a model where out of all datasets, only a selected subset are first decomposed to provide regressors that sufficiently estimate sources across all datasets. These regressors define a per-source cost function that naturally extends independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G), a powerful formulation for exploiting cross-dataset dependencies. Using simulated and real fMRI data, we demonstrate significant advantages of this method compared with other JBSS methods.

Identification of subgroups of subjects homogeneous functional networks is a key step for precision medicine. Independent vector analysis (IVA) is shown to be effective for this task, however, it has a substantial computing cost. We propose a constrained independent component analysis algorithm based on minimizing the entropy bound (c-EBM) to overcome the computational complexity limitation of IVA. A set of spatial maps used as constraints provides a connection across the datasets, provides alignment across subject-wise ICA analyses and serves as a foundation for subgroup identification. The approach makes use of the available prior knowledge while allowing flexible density modeling without an orthogonality requirement for the demixing matrix. Synthetic data and large scale multi-subject resting state fMRI data have both been used to evaluate the performance of the new algorithm, c-EBM. The findings demonstrate that c-EBM is adaptable in terms of various settings for the constraint parameter on the synthetic data. With multi-subject resting state fMRI data, c-EBM can effectively identify subgroups and discover meaningful brain networks that show significant group differences between subgroups.

Data fusion—the joint analysis of multiple datasets—through coupled factorizations has the promise to enable enhanced knowledge discovery, and hence is an active area. Various formulations of coupled matrix factorizations have been proposed, each with its own modeling assumptions. In this paper, we study two such methods, namely Independent Vector Analysis (IVA), i.e., extension of Independent Component Analysis (ICA) to multiple datasets, and PARAFAC2, a tensor factorization approach. We demonstrate the modeling assumptions of IVA and PARAFAC2 using simulations, revealing that both methods can accurately capture the latent components, albeit with certain differences in capturing the corresponding subject scores. By making use of a rich multi-task functional Magnetic Resonance Imaging (fMRI) dataset, we show how the two methods can be used for achieving two important goals at once, namely capturing group differences between patients with schizophrenia and healthy controls with interpretable components, as well as understanding the relationship across multiple tasks. This is achieved through the definition of source component vectors across datasets.

Identification of homogeneous subgroups of subjects plays a key role in the study of precision medicine. While there are a number of approaches based on the clustering of low-level features such as behavioral variables, work that makes use of fully multivariate nature of medical imaging data is very limited. Given that the individual variability in brain functional networks obtained from functional magnetic resonance imaging (fMRI) data is noted as being both significant and consistent like fingerprints, its use provides a particularly appealing approach to this challenging problem. We present a completely data-driven approach, subgroup identification using independent vector analysis (SI-IVA), which leverages the desirable properties of IVA to uncover the relationship across subjects along with the discovery of subgroup structures revealed by Gershgorin disc theorem. We show that SI-IVA outperforms an eigenanalysis-based approach by simulations. We then apply the method to real fMRI data obtained from patients of during resting state to identify group differences in multiple relevant brain regions including primary somatosensory and motor cortex, which demonstrates that SI-IVA provides interpretable and meaningful results.

Given the prevalence of independent component analysis (ICA) for signal processing, many methods for improving the convergence properties of ICA have been introduced. The most utilized methods operate by iterative rotations over pre-whitened data, whereby limiting the space of estimated demixing matrices to those that are orthogonal. However, a proof of the identifiability conditions for orthogonal ICA methods has not yet been presented in the literature. In this paper, we derive the identifiability conditions, starting from the orthogonal ICA maximum likelihood cost function. We then review efficient optimization approaches for orthogonal ICA defined on the Lie group of orthogonal matrices. Afterwards, we derive a new efficient algorithm for orthogonal ICA, by defining a mapping onto a space of constrained matrices which we define as hyper skew-symmetric. Finally, we experimentally demonstrate the advantages of the new algorithm over the pre-existing Lie group methods.

Methods based on independent component analysis (ICA) and canonical correlation analysis (CCA) as well as their various extensions have become popular for the fusion of multimodal data as they minimize assumptions about the relationships among multiple datasets. Two important extensions that are widely used, joint ICA (jICA) and parallel ICA (pICA), make a number of simplifying assumptions that might limit their usefulness such as identical mixing matrices for jICA, and the requirement for the same number of components for jICA and pICA. In this paper, we propose a new, flexible hybrid method for fusion based on ICA and CCA, called consecutive independence and correlation transform (C-ICT), which relaxes the main limitations of jICA and pICA. We demonstrate performance advantages of C-ICT both through simulations and application to real medical data collected from schizophrenia patients and healthy controls performing an auditory oddball task (AOD).