Mohammad Abu Baker Siddique Akhonda

Joint blind source separation (JBSS) is a powerful methodology for analyzing multiple related datasets, able to jointly extract sources that describe statistical dependencies across the datasets. However, JBSS can be computationally prohibitive with high-dimensional data, thus there exists a key need for more efficient JBSS algorithms. JBSS algorithms typically rely on numerical solutions, which may be expensive due to their iterative nature. In contrast, analytic solutions follow consistent procedures that are often less expensive. In this paper, we introduce an efficient analytic solution for JBSS. Denoting a set of sources dependent across the datasets as a “source component vector” (SCV), our solution minimizes correlation among separate SCVs by minimizing distance of the SCV cross-covariance’s eigenvector matrix from a block diagonal matrix. Under the orthogonality constraint, this leads to a system of linear equations wherein each subproblem has an analytic solution. We derive identifiability conditions of our solution’s estimator, and demonstrate estimation performance and time efficiency in comparison with other JBSS algorithms that exploit source correlation across datasets. Results demonstrate that our solution achieves the lowest asymptotic computational complexity among JBSS algorithms, and is capable of superior estimation performance compared with algorithms of similar complexity.

Joint blind source separation (JBSS) has wide applications in modeling latent structures across multiple related datasets. However, JBSS is computationally prohibitive with high-dimensional data, limiting the number of datasets that can be included in a tractable analysis. Furthermore, JBSS may not be effective if the data’s true latent dimensionality is not adequately modeled, where severe overparameterization may lead to poor separation and time performance. In this paper, we propose a scalable JBSS method by modeling and separating the “shared” subspace from the data. The shared subspace is defined as the subset of latent sources that exists across all datasets, represented by groups of sources that collectively form a low-rank structure. Our method first provides the efficient initialization of the independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G) specifically designed to estimate the shared sources. Estimated sources are then evaluated regarding whether they are shared, upon which further JBSS is applied separately to the shared and non-shared sources. This provides an effective means to reduce the dimensionality of the problem, improving analyses with larger numbers of datasets. We apply our method to resting-state fMRI datasets, demonstrating that our method can achieve an excellent estimation performance with significantly reduced computational costs.

It is becoming increasingly common to collect multiple related neuroimaging datasets either from different modalities or from different tasks and conditions. In addition, we have non-imaging data such as cognitive or behavioral variables, and it is through the association of these two sets of data—neuroimaging and non-neuroimaging—that we can understand and explain the evolution of neural and cognitive processes, and predict outcomes for intervention and treatment. Multiple methods for the joint analysis or fusion of multiple neuroimaging datasets or modalities exist; however, methods for the joint analysis of imaging and non-imaging data are still in their infancy. Current approaches for identifying brain networks related to cognitive assessments are still largely based on simple one-to-one correlation analyses and do not use the cross information available across multiple datasets. This work proposes two approaches based on independent vector analysis (IVA) to jointly analyze the imaging datasets and behavioral variables such that multivariate relationships across imaging data and behavioral features can be identified. The simulation results show that our proposed methods provide better accuracy in identifying associations across imaging and behavioral components than current approaches. With functional magnetic resonance imaging (fMRI) task data collected from 138 healthy controls and 109 patients with schizophrenia, results reveal that the central executive network (CEN) estimated in multiple datasets shows a strong correlation with the behavioral variable that measures working memory, a result that is not identified by traditional approaches. Most of the identified fMRI maps also show significant differences in activations across healthy controls and patients potentially providing a useful signature of mental disorders.

Brain signals can be measured using multiple imaging modalities, such as magnetic resonance imaging (MRI)-based techniques. Different modalities convey distinct yet complementary information; thus, their joint analyses can provide valuable insight into how the brain functions in both healthy and diseased conditions. Data-driven approaches have proven most useful for multimodal fusion as they minimize assumptions imposed on the data, and there are a number of methods that have been developed to uncover relationships across modalities. However, none of these methods, to the best of our knowledge, can discover “one-to-many associations”, meaning one component from one modality is linked with more than one component from another modality. However, such “one-to-many associations” are likely to exist, since the same brain region can be involved in multiple neurological processes. Additionally, most existing data fusion methods require the signal subspace order to be identical for all modalities—a severe restriction for real-world data of different modalities. Here, we propose a new fusion technique—the consecutive independence and correlation transform (C-ICT) model—which successively performs independent component analysis and independent vector analysis and is uniquely flexible in terms of the number of datasets, signal subspace order, and the opportunity to find “one-to-many associations”. We apply C-ICT to fuse diffusion MRI, structural MRI, and functional MRI datasets collected from healthy controls (HCs) and patients with schizophrenia (SZs). We identify six interpretable triplets of components, each of which consists of three associated components from the three modalities. Besides, components from these triplets that show significant group differences between the HCs and SZs are identified, which could be seen as putative biomarkers in schizophrenia.