  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.
