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Given a set of vectors, lets say that each coordinate is populated from an alphabet (meaning set of symbols, numbers, etc) (particular or shared alphabets are indistinct).

Is there any standard procedure for performing the following task ?

Look for sets of positions that "make the same choice" in several vectors.

That means: a subset of indices where, when we project to just those indices, there's some value that's taken on by many of the vectors.

An example:

Input                 
[0,-,0]
[0,+,+]
[+,+,+]
[0,0,0]
[-,+,+]

Output

2 coordinates involved ( 2 and 3), appearing in 3 vectors: x2=+ and x3=+
1 coordinate involved (1), appearing in 2 vectors:  x1=0
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    $\begingroup$ Can you define what you mean by correlation, in this context? (I can invent some possible meanings and then answer under that particular meaning, but it would be more useful for you to define what you mean by correlation, so that answers match what you are looking for.) $\endgroup$ – D.W. May 6 '16 at 5:07
  • $\begingroup$ Yes, of course. One of my short comings is not knowing the computer science /machine learning speech, so thanks for discussing this with me. When I say inputs are vectors I mean that "positions matter". For each coordinate of the vectors, there is a certain "alphabet" (set of candidate symbols) (In the case I presented in the question, this alphabet is the same for all coordinates). I'm looking for the fact that several coordinates "make the same choice" -regardless of what that "choice" is- in several vectors. $\endgroup$ – cladelpino May 7 '16 at 20:02
  • $\begingroup$ I was hoping to make a "super alphabet" unioning the alphabets of every coordinate (labeled for each coordinate), so that now each vector is a subset of this super alphabet, and looking for frequent closed itemsets. $\endgroup$ – cladelpino May 7 '16 at 20:05
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A possible solution would be generating (in Apriori terms) a "transaction" that contains indexed symbols and mine that for frequent itemsets.

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