Non-Gaussian Penalized PARAFAC Analysis for fMRI Data - Liang, Jingsai; Zou, Jiancheng; Hong, Don (Frontiers in Applied Mathematics and Statistics, 2019)
Independent Component Analysis (ICA) method has been used widely and successfully in functional magnetic resonance imaging (fMRI) data analysis for both single and group subjects. As an extension of the ICA, tensorial probabilistic ICA (TPICA) is used to decompose fMRI group data into three modes: subject, temporal and spatial. However, due to the independent constraint of the spatial components, TPICA is not very efficient in the presence of overlapping of active regions of different spatial components. Parallel factor analysis (PARAFAC) is another method used to process three-mode data and can be solved by alternating least-squares. PARAFAC may converge into some degenerate solutions if the matrix of one mode is collinear. It is reasonable to find significant collinear relationships within subject mode of two similar subjects in group fMRI data. Thus, both TPICA and PARAFAC have unavoidable drawbacks. In this paper, we try to alleviate both overlapping and collinearity issues by integrating the characters of PARAFAC and TPICA together by imposing a non-Gaussian penalty term to each spatial component under the PARAFAC framework. This proposed algorithm can then regulate the spatial components, as the high non-Gaussianity can possible avoid the degenerate solutions aroused by collinearity issue, and eliminate the independent constraint of the spatial components to bypass the overlapping issue. The algorithm outperforms TPICA and PARAFAC on the simulation data. The results of this algorithm on real fMRI data are also consistent with other algorithms.