ENH: combined gradiometers (plotting + stats)

[kingjr]

@dengemann @agramfort Continuing on our email discussion... As I said, the pairs of gradiometers can be combined to get a 2D vector, and hence be treated as a single dependent variable.

In terms of plotting this could be translated into a 3D color plot where hues indicate the combined gradiometers orientations, and light to the norm of the vector.

For example (made from Matlab sorry...):

and in terms of topography

With such view i) you're closer to what you record and (and actually appreciate the complexity of the collected data). ii) you can tell when you have an inversion of polarity (although this is generally directly visible with magnetometers). For example, in http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0085791, we observed a sign reversal of the topographical pattern using MVPA. While the norm of combined gradiometers is obviously blind to such thing.

Regarding statistics, that would be nice to apply a single analysis using both the angle and the norm differ across two conditions, as i) you would keep all information (unlike when you use the norm) ii) you would reduce the number of tests (unlike a single statistical test per gradiometer). I haven't found such analysis yet. You could off course test this separately using circular analysis for the angle.

Philipp Berens suggested me to use bootstrapping for testing both at once, but on my computer that rapidly became unpractical using so many sensors and time points.

An interesting follow up question could then be related to the time frequency transform applied to such vector.