Joint blind source separation (JBSS) is a powerful framework for extracting latent sources from multiple datasets while keeping their coherence across multiple linked datasets. Algorithms for JBSS, while offering the capability of improved estimation performance, often incur high computational complexity and hence are not scalable to studies with hundreds or thousands of datasets. In this paper, we propose a simple yet efficient method for source separation that exploits both the correlation among sources within each dataset and across the datasets. The proposed method, named reference-guided component analysis (RGCA), uses source templates as references to (i) guide the separation of sources on each dataset and (ii) establish source dependence and automatically align them across the datasets. In addition, we promote independence among latent sources within each dataset by adding orthogonal constraints on the demixing vectors. The resulting optimization admits an analytic solution that enables extremely fast implementation of RGCA. Our numerical results demonstrate that RGCA obtains competitive performance while having a runtime far superior to other JBSS methods. The proposed method provides a robust and scalable solution to multi-subject functional magnetic resonance imaging (fMRI) studies, enabling joint analysis of thousands of subjects within a few minutes.

Independent vector analysis (IVA) generalizes independent component analysis (ICA) to multiple datasets, and when used with a multivariate Gaussian model (IVA-G), provides a powerful tool for joint analysis of multiple datasets in an array of applications. While IVA-G enjoys uniqueness guarantees, the current solution to the problem exhibits significant variability across runs necessitating the use of a scheme for selecting the most consistent one, which is costly. In this paper, we present a penalized maximum-likelihood framework for the problem, which enables us to derive a non-convex cost function that depends on the precision matrices of the source component vectors, the main mechanism by which IVA-G leverages correlation across the datasets. By adding a quadratic regularization, a block-coordinate proximal algorithm is shown to offer a suitable solution to this minimization problem. The proposed method also provides convergence guarantees that are lacking in other state-of-the-art approaches to the problem. This also allows us to obtain overall slightly better performance, and in particular, we show that our method yields better estimation in average than the current IVA-G algorithm for various source numbers, datasets, and degrees of correlation across the data.

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.

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.

Independent component analysis (ICA) has found wide application in a variety of areas, and analysis of functional magnetic resonance imaging (fMRI) data has been a particularly fruitful one. Maximum likelihood provides a natural formuiation for ICA and allows one to take into account multiple statistical properties of the data-forms of diversity. While use of multiple types of diversity allows for additional flexibility, it comes at a cost, leading to high variability in the solution space. In this paper, using simulated as well as fMRI-like data, we provide insight into the trade-offs between estimation accuracy and algorithmic consistency with or without deviations from the assumed model and assumptions such as the statistical independence. Additionally, we propose a new metric, cross inter-symbol interference, to quantify the consistency of an algorithm across different runs, and demonstrate its desirable performance for selecting consistent run compared to other metrics used for the task.