image feature extraction
I may be wrong if i have not understood the question! I am trying to give a rather elementary introduction here. I can refine things and be more rigorous as suited. 



What you are looking for is that of 100 (or 1000) patches, which patch is the most representative patch of all.  

For simplicity if the size of a patch is 1x1. So it is just a scalar. In this case, you can just find a simple average $RepScalar = Avg = \sum P_i$. 

You can also apply median rather than averaging if appropriate. A more generalized way is to treat this as random variable and find expected value as $E(P) = \sum PDF(x) \cdot x $

I don't know if you are really conversent with this: so i am leaving you with a tutorial on this: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter6.pdf

Now in your case the $P$ is a vector instead of scalar. 

So the averaging will become 

$$
RepPatch[i] = \sum_{k} P_k[i]   
$$

where $k$ is a patch number and $i \in { 1, ... 100 }$ for $10x10$ patch size. 

If you know the PDF or if you can estimate PDF you can find Expected value of this but for a vector of size of 100 (10x10) it is too complex.