Abstract
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.
Highlights
Independent Component Analysis (ICA) is one of the most popular methods to analyze functional magnetic resonance imaging (fMRI) single or group data especially when the time courses are not available [1,2,3,4], such as the application of autism experiments [5]
This proposed algorithm can overcome the overlapping issue because it is still based on the Parallel factor analysis (PARAFAC), which does not need the independent constraint of the spatial components
Repeat until the value of object function (21) is reduced by new aj, where aj. This proposed algorithm can overcome the overlapping issue because it is still based on the PARAFAC framework, which does not need the independent constraint of the spatial components
Summary
ICA is one of the most popular methods to analyze fMRI single or group data especially when the time courses are not available [1,2,3,4], such as the application of autism experiments [5]. Without the consideration of the independent constraint among spatial components, PARAFAC can outperform TPICA in the presence of overlapping of activate regions in the spatial mode Both TPICA and PARAFAC have advantages and disadvantages in processing fMRI data. In this paper, inspired by the method of penalty based PARAFAC, via imposing a non-Gaussian penalty term for the spatial components within the PARAFAC, we propose an algorithm that combines advantages and eliminates disadvantages of both TPICA and PARAFAC simultaneously. In the case of collinearity issues, the degenerate solution of spatial components can be alleviated because the non-Gaussian penalty term can regulate each spatial component to be as non-Gaussian as possible This proposed algorithm can overcome the overlapping issue because it is still based on the PARAFAC, which does not need the independent constraint of the spatial components.
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