W-shingling

In natural language processing a w-shingling is a set of unique ''shingles each of which is composed of contiguous subsequences of tokens within a document, which can then be used to ascertain the similarity between documents. The symbol w'' denotes the quantity of tokens in each shingle selected, or solved for.
The document, "a rose is a rose is a rose" can therefore be maximally tokenized as follows:
The set of all contiguous sequences of 4 tokens is
Which can then be reduced, or maximally shingled in this particular instance to

Resemblance

For a given shingle size, the degree to which two documents A and B resemble each other can be expressed as the ratio of the magnitudes of their shinglings' intersection and union, or
where |A| is the size of set A. The resemblance is a number in the range , where 1 indicates that two documents are identical. This definition is identical with the Jaccard coefficient describing similarity and diversity of sample sets.