Joint, Partially-joint, and Individual Independent Component Analysis in Multi-Subject fMRI Data

Objective: Joint analysis of multi-subject brain imaging datasets has wide applications in biomedical engineering. In these datasets, some sources belong to all subjects (joint), a subset of subjects (partially-joint), or a single subject (individual). In this paper, this source model is referred to as joint/partially-joint/individual multiple datasets multidimensional (JpJI-MDM), and accordingly, a source extraction method is developed. Method: We present a deflation-based algorithm utilizing higher order cumulants to analyze the JpJI-MDM source model. The algorithm maximizes a cost function which leads to an eigenvalue problem solved with thin-SVD (singular value decomposition) factorization. Furthermore, we introduce the JpJI-feature which indicates the spatial shape of each source and the amount of its jointness with other subjects. We use this feature to determine the type of sources. Results: We evaluate our algorithm by analyzing simulated data and two real functional magnetic resonance imaging (fMRI) datasets. In our simulation study, we will show that the proposed algorithm determines the type of sources with the accuracy of 95% and 100% for 2-class and 3-class clustering scenarios, respectively. Furthermore, our algorithm extracts meaningful joint and partially-joint sources from the two real datasets, which are consistent with the existing neuroscience studies. Conclusion: Our results in analyzing the real datasets reveal that both datasets follow the JpJI-MDM source model. This source model improves the accuracy of source extraction methods developed for multi-subject datasets. Significance: The proposed joint blind source separation algorithm is robust and avoids parameters which are difficult to fine-tune.