Understanding how ERPimages and topographies represent MEEG components

In EEGlab and other MEEG toolboxes, we often represent “components” like this:

The "ERPimage" (that's how they call it) on the right is just a different way of displaying a time-course.

Let us illustrate how this is built:

Say you have these 100 "trials" on one channel shown on top of each other here:

That's a 100 lines on top of each other. Not very easy to see anything.

If we spread them vertically, we get this.

Ok? this is exactly the same thing as above, just each trial is on one line now, instead of having them all exactly on top of each other. The vertical scale is also changed (squeezed) so they don't look too large and overlap with each other.

Now if instead of using black lines, we use colored rows of pixels, we get this:

The first row at the bottom is blue whenever the potential is low on the first trial, and yellow whenever the potential is high on that trial.
Now just to show you, if I add 10µV to the data on trial 10 between time 0 and 100ms, I get this:

See?

Now this kind of display is possible to do for any time course. It could be one channel, like in the plots above, but just as well, say for the average of two channels, or the opposite of one channel plus another one or whatever combination of channels you like to display.

One way of representing which channels I include in this is to use a topographical map.

If I'm showing just one channel, then the associated topography is just a green topo with red at that one channel (like the component you sent me earlier).

like this:

Note that the map is interpolated. The actual values in this map are zero everywhere, and 1 at channel 10. There is no green to red dégradé in the actual data.

If I'm showing the average of two channels, then the topography will have just two channels in red. It would look something like this:

Here I just set channels number 10 and 20 to a value of 1, and everything else to zero. If this were an ICA component, we would say that this component "weighs" on channels 10 and 20 only. The ERPimage would represent the average of the two channels exactly.

If I want to represent a time course that takes 1 x [channel #10] -1 x [channel #20], it will look like this:

Now in the case of that component:

We are looking at a component that weighs mostly on the left posterior channels (channels are not represented as dots in this map, but you can imagine them). The time course shown on the right as an ERPimage corresponds to the weighted average of those posterior channels (and a bit of a negative weight on frontal channels, as you see from the blueish color up there). Underneath the ERPimage, the blue line shows the average time-course of that component across trials.