I am seeking some directions for a proper path to research the solve for this problem:
My company made all our employees take a "StrengthFinders" test, which results in every employee being assigned their top five (ordered) "strengths" from a possible list of 34 strengths. We have 500 employees. I am supposed to identify all the employees that match each other for the same 5 strengths (order not important), and also for employees that match each other for 4 out of 5 strengths (again, order doesn't matter). I could potentially have multiple groups matching on different sets of strengths, e.g.: Group 1: Billy, Sally, Michael have strengths A, H, I, K, Z Group 2: Bobby and Suzy have strengths A, B, L, S, W
For the case where strengths match for 4 out of 5, I might have the same people from Group 1 above, plus Joe, whose strengths are A, H, M, K, Z; and Seth, whose strengths are A, H, G, K, Z. I would expect more groupings for the case of 4 out of 5 than the 5 out of 5 case.
The strengths are categorical in nature, so what I've read so far has largely revolved around clustering of continuous numerical variables.
I am looking for an algorithmic way to identify clusters and the members of those clusters for this situation. I think I could do this brute force by repeatedly sorting data in Excel, but I'm confident that a better way must exist, and I ask you to point me in that direction. Thank you.