One limitation to ICA approaches is that they cannot determine the number of appropriate components to decompose the data or their ordering. The number of components chosen is important as one too many may result in incorporating noisy sources and too few may mix the signals together. To determine the appropriate number of components, we used two different stopping methods applied to the eigenspectrum derived from PCA (13).The first stopping method is a measure of separability of the eigenvalues (λi), where we used a standard rule of thumb (36) to assess which eigenvalues (λi) exceed that expected from a random process. If the separation between eigenvalues (Δλi = λi − λi−1, for i > 1) falls below the uncertainty ∂λi = λi(2/n)2, then the component becomes more difficult to separate from its neighbor and from noise. The second approach uses Horn’s parallel analysis (37), a Monte Carlo simulation approach that randomly scrambles the data to create a suite of random samples and its simulated eigenspectrum and their uncertainties. If the observed λi exceeds the 95% confidence interval of the simulated λi, then the component is retained. We found that both methods indicate that four PCs are significant, and we used this number to decompose the data.

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