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iscovering 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. 

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 formulation 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. 

Abstract Despite the known benefits of data‐driven approaches, the lack of approaches for identifying functional neuroimaging patterns that capture both individual variations and inter‐subject correspondence limits the clinical utility of rsfMRI and its application to single‐subject analyses. Here, using rsfMRI data from over 100k individuals across private and public datasets, we identify replicable multi‐spatial‐scale canonical intrinsic connectivity network (ICN) templates via the use of multi‐model‐order independent component analysis (ICA). We also study the feasibility of estimating subject‐specific ICNs via spatially constrained ICA. The results show that the subject‐level ICN estimations vary as a function of the ICN itself, the data length, and the spatial resolution. In general, large‐scale ICNs require less data to achieve specific levels of (within‐ and between‐subject) spatial similarity with their templates. Importantly, increasing data length can reduce an ICN's subject‐level specificity, suggesting longer scans may not always be desirable. We also find a positive linear relationship between data length and spatial smoothness (possibly due to averaging over intrinsic dynamics), suggesting studies examining optimized data length should consider spatial smoothness. Finally, consistency in spatial similarity between ICNs estimated using the full data and subsets across different data lengths suggests lower within‐subject spatial similarity in shorter data is not wholly defined by lower reliability in ICN estimates, but may be an indication of meaningful brain dynamics which average out as data length increases.