Calculating chance level accuracy I have the following problem from computational neuroscience (presented here if you are interested in the main source):

For 126 subjects, the brain activity in 268 regions of the brain is measured (one time series per region). Then a correlation matrix is computed out of this measured time series (i.e. a symmetric 268 * 268 matrix). The same thing is done on two days, so we have 2 such matrices for each subject.
Now, we take iteratively one matrix of one particular subject from day 1 ("target matrix"), and compute the correlation between this matrix and all the 126 matrices of day 2. The highest correlation value between the target matrix and the matrices of day 2 is used to identify the matrix from day 2 which belongs to the same subject who's correlation matrix (from day 1) we are using as the "target matrix".This process is done 126 times (i.e. at each iteration, another person's day 1 matrix is used as the target matrix).

I have the two following questions now:
(1) Are these trials (finding the subject from the target matrix also on day 2) dependent from each other? If so, why?
(2) How can we calculate chance level accuracy, i.e. if it would be pure guessing to pick out the correct matrix from day 2, what number of correct guesses can we expect? Is there any way to determine that?
Thanks
 A: Some remarks. 1. At the end of iteration 1, you get the couple $(1,a_1)$. For the second iteration you have to keep all the $126$ matrices of day-2 (in particular don't remove $a_1$); this is essential if you want that the obtained correspondences are independent from each other (your question (1)).
Answer to (2): at the end of the process: if your match is far from being injective, then your method should be rejected. If your match is almost injective, then you only have to reconsider some cases.


*Methodology: you control the brain activity of $126$ subjects; is the required work unusual for the observed people ? If YES, then some people understand more quickly than others; for these, the interactions in the brain regions may vary from one day to another. In general, learning skills involved in this type of study.

*Conversely, specialized questions  (one knows immediately, or we do not know at all) make it easier to recognize a subject among others: rap music, technology car engines, running, haschich....

*In fact, I don't understand the following point: the interactions between brain regions vary (for a same people) with the question or the proposed act. How, in these conditions, to obtain some time series that has a cognitive sense ? Do you request a variation of the same question or of the same act ?
