A critique of Tensor Probabilistic Independent Component Analysis: implications and recommendations for multi-subject...

Tensor Probabilistic Independent Component Analysis (TPICA) is a popular tool for analyzing multi-subject fMRI data (voxels×time×subjects) because of TPICA's supposed robustness. In this paper, we show that TPICA is not as robust as its authors claim. Specifically, we discuss why TPICA's overall objective is questionable, and we present some flaws related to the iterative nature of the TPICA algorithm. To demonstrate the relevance of these issues, we present a simulation study that compares TPICA versus Parallel Factor Analysis (Parafac) for analyzing simulated multi-subject fMRI data. Our simulation results demonstrate that TPICA produces a systematic bias that increases with the spatial correlation between the true components, and that the quality of the TPICA solution depends on the chosen ICA algorithm and iteration scheme. Thus, TPICA is not robust to small-to-moderate deviations from the model's spatial independence assumption. In contrast, Parafac produces unbiased estimates regardless of the spatial correlation between the true components, and Parafac with orthogonality-constrained voxel maps produces smaller biases than TPICA when the true voxel maps are moderately correlated. As a result, Parafac should be preferred for the analysis multi-subject fMRI data where the underlying components may have spatially overlapping voxel activation patterns.