However these permutations are not sufficient to estimate


One might expect that we could estimate the Jaccard similarity of columns without using all possible permutations of rows. For example, we could only allow cyclic permutations; i.e., start at a randomly chosen row r, which becomes the first in the order, followed by rows r + 1, r + 2, and so on, down to the last row, and then continuing with the first row, second row, and so on, down to row r - 1. There are only n such permutations if there are n rows. However, these permutations are not sufficient to estimate the Jaccard similarity correctly. Give an example of a two-column matrix where averaging over all the cyclic permutations does not give the Jaccard similarity.

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Basic Computer Science: However these permutations are not sufficient to estimate
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