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Canonical Response Parameterization: Quantifying the structure of responses to single-pulse intracranial electrical brain stimulation
Fig 8
Illustrations of different normalizations of single-trial cross projections.
As discussed in the manuscript, different trials Vk(t) and Vl(t) may be compared with each other directly, or after normalization with 
. A. Un-normalized projections Vk(t)Vl(t) are sub-optimal because trials with large amplitude are over-emphasized in comparison with trials of lower amplitude but more characteristic structure. B. The time-resolved structure of fully-normalized projections 
are sub-optimal because they dramatically favor early transients and cannot resolve temporally-sustained structure. C. Semi-normalized projections are optimal in that they balance emphasis of amplitude and sustained structure between trials. Panels D-F show the same sample data as A-C, and illustrate the effect of extracting the canonical response from different epochs of time. In the “standard” extraction approach we have illustrated so far, C(t) is discovered using linear kernel PCA from V(t) over the isolated time interval from t1 to τR (black line with yellow highlight). We can also unit normalize the average voltage 
over the t1 to τR interval, though the explained variance and signal-to-noise are slightly worse. D. If a C(t) is extracted using linear kernel PCA from t1 to t2 = 3 s (blue+red compound trace), the explained variance and signal-to-noise is very poor due to the introduction into the algorithmic process of a large amount of unnecessary noise from the time following τR, even if the extracted form is truncated at τR for parameterization (red trace). E and F. As in (D), but for t2 = 2 s (E) and t2 = 1 s (F). Note how the shapes converge as t2 decreases.
doi: https://doi.org/10.1371/journal.pcbi.1011105.g008