What are "linear spatial weightings" and "specific temporal windows" in Philiastides & Sajda (2006)? I am undergraduate student in mathematics and a complete beginner in the field of neuroscience. I recently started a project in Mathematical biology which brought me to the above mentioned paper. I couldn't understand what is meant by the "linear spatial weightings" and "specific temporal windows" in the following passage :


  "We used a machine learning approach to identify linear spatial
  weightings of the EEG sensors for specific temporal windows which
  optimally discriminate between target (faces) and non-target (cars)
  trials."


I would really appreciate if someone could break these things down in simpler terms and if possible suggest me some sources to refer.
( I was wondering if the 'linear spatial weightings' here is similar to the concept of 'Center of mass' which can be said as 'linear spatial weightings' of mass; just a guess.And the 'specific temporal windows' is some continuous range in the 'time taken' (to respond to stimulus) axis. Again, only a guess.)

References


Philiastides, M. G., &amp; Sajda, P. (2006). Temporal characterization of the neural correlates of perceptual decision making in the human brain. Cerebral Cortex, 16(4), 509-518.
I can make a guess, until someone who really knows the answer comes along :) I haven't read the paper and the answer I can give is probably not going to be formal enough for a math student. But I can tell you what I think.

The goal of the paper, I'm guessing, is to look at the pattern of activation recorded by EEG when viewing pictures of faces and cars, and to try to say if the two activity patterns differ. One way to so this is to show some faces and cars, look at EEG activity and tell your algorithm which is which. Then, after a training period, let your algorithm classify future input into faces and cars as well as it can. In the end, you want to see if it can classify above chance. If yes, then you can say with certainty that the pattern of neural activity between cars and faces differs. 

You might then wonder how it differs. If this guesswork is correct, then temporal windows refers to moments in time when this pattern classification works best - for example, 150-200 milliseconds after the picture was displayed. This can tell you something about how much visual processing must happen before objects are seen as belonging to a certain category. If not done properly, though, you might just be detecting simple visual differences such as amount of information in a certain frequency band - not very exciting. A very early temporal window of best performance of your classifier algorithm would indicate that this is the case. In any case, you learn something from seeing where the best temporal window is.

Spatial weightings of the sensors refers to the difference in activity recorded in each of the individual EEG sensors. From that, you might infer that the difference between cars and faces is most prominent in, say,  frontal sensors, which gives you a hint about the possible brain areas involved in category classification. The linear I don't know what to make of unfortunately. It refers to the bit of the algorithm that decides how to classify these spatial patterns, perhaps by relying on how neural activity is spread over a distance (i.e. how activity originating at a certain place will be captured by the sensor just above it, and how by sensors further away), but to know what makes it linear, you would really need to see the algorithm. 

Hope this helps!