Revisiting Polarity Indeterminacy of ICA-Decomposed ERPs and Scalp Topographies

We propose an alternative method to align the polarities of independent components (ICs) for group-level IC cluster analysis. Current methods are presently limited in how indeterminacy of IC polarities is handled, as when multiplying a weight matrix to a time-series IC activation, the result from 1 × 1 and - 1 × - 1 are indistinguishable. We first clarify the EEGLAB's default solution and define it as the iterative correlation maximization as it maximizes the within-cluster correlations of the IC scalp topographies to the cluster mean. We then propose the covariance maximization method, which determines the polarity of ICs based on the sign of the largest eigenvalue of covariance matrix. We compared the two methods on datasets from a published visual event-related potential (ERP) study. The results were similar when both methods were applied to the IC scalp topographies. However, when the proposed method was applied to IC ERPs, the number of clusters that showed significant ERP amplitudes increased from 5 to 9 out of 9 due to minimization of within-cluster ERP amplitude cancellation. Our study confirm covariance maximization provides an alternative solution to post-ICA group-level analysis that can maximize sensitivity of IC ERPs.