ICA’s bug: How ghost ICs emerge from effective rank deficiency caused by EEG electrode interpolation and incorrect re-referencing - Kim, Hyeonseok; Luo, Justin; Chu, Shannon; Cannard, Cedric; Hoffmann, Sven; Miyakoshi, Makoto (Frontiers in Signal Processing, 2023)
Independent component analysis (ICA) has been widely used for electroencephalography (EEG) analyses. However, ICA performance relies on several crucial assumptions about the data. We focus here on the granularity of data rank, the number of linearly independent EEG channels. When the data are rank-full (i.e., all channels are independent), ICA produces as many independent components (ICs) as the number of input channels (rank-full decomposition). However, when the input data is rank-deficient, as is the case with bridged or interpolated electrodes for example, ICA produces the same number of ICs as the data rank (forced rank-deficiency decomposition), introducing undesired ghost ICs like a bug of ICA. We show that the ghost ICs have white-noise properties in both time and frequency domains while maintaining surprisingly typical scalp topographies, and can therefore be easily missed by EEG researchers and affect findings in unknown ways. This problem occurs when the minimum eigenvalue λ_min of the input data is smaller than a certain threshold, leading to matrix inversion failure as if the rank-deficient inversion was forced, even if the data rank is cleanly deficient by one. We define this problem here as the effective rank deficiency. Using sound file mixing simulations, we first demonstrate the effective rank deficiency problem and determine that the critical threshold for λ_min is 10-7 in the given situation. Second, we use empirical EEG data to show how two preprocessing stages, re-referencing to average without including the initial reference and non-linear electrode interpolation cause this forced rank-deficiency problem. Finally, we show that the effective rank deficiency problem can be solved by using the identified threshold ( λ_min = 10-7) and the correct re-referencing procedure described here. The former ensures achieving effective rank-full decomposition by properly reducing the input data rank, and the latter by avoiding a widely practiced incorrect re-referencing approach. We discuss the ambiguous status of the initial reference electrode in literature when re-referencing. We make our data and code available to facilitate the implementation of our recommendations for the EEG community.