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POComparing boolean matrices
 

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    <p>I have a little problem. I need to compare one two-dimensional array filled with ones and zeros (lets call it Matrix A - zeros actually represent blank spots and ones are positions of football players on the field) against lots of other matrices filled differently (but again, just ones and zeros) and the result should be some indication which of the matrices is most similar with the Matrix A. By similarity I mean similarity in distribution (or positioning) of the players on the field - so the matrix with players postition the most similar to the matrix A will be chosen for further stuff. </p> <p>Could somebody help with this algorithmic problem ? </p> <p>I'm writing it in c++ but pseudo-code would suffice. The problem is just a comparison algorithm. The best would be if the output of the comparison function would be something like <code>similarity coefficient</code> which I can store in an array and later choose the most similar matrix using it. But I just cant come up with some algorithm for that similarity comparison. </p> <p>EDIT: some clarifications about similarity and algorithm copied from my comments below - </p> <p>Matrix A - <a href="http://www2.wolframalpha.com/input/?i=%7B%7B1,0,0%7D,%7B0,0,0%7D,%7B0,0,0%7D%7D" rel="nofollow">Matrix A</a> , Matrix 1 - <a href="http://www2.wolframalpha.com/input/?i=%7B%7B0,0,0%7D,%7B0,0,0%7D,%7B0,0,1%7D%7D" rel="nofollow">Matrix1</a> , Matrix 2 - <a href="http://www2.wolframalpha.com/input/?i=%7B%7B0,0,0%7D,%7B0,1,0%7D,%7B0,0,0%7D%7D" rel="nofollow">Matrix2</a>, Both have 1 change in comparison with Matrix A, but for me - matrix 2 must be "more similar" - because player is standing closer to its position in matrix A</p> <p>Matrices are considered to be around 8x6 or something like that, it needs to be reasonably fast - it will be computed every game cycle (so every 20ms or so..), and there will be 5 players on each side. </p>
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    1. COYou're going to need to define "similarity" a lot more robustly than the above vague description if you want to come up with an algorithm
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    2. COWell the most similar matrix would be the one with the players standing closest to the positions (or in some cases exactly on the positions) in the Matrix A.
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    3. COMaybe it would help if you added some examples to your question, along with the required "similarity" measure that you would expect in each case ?
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