In natural language processing a w-shingling is a set of unique "shingles" (n-grams, contiguous subsequences of tokens in a document) that can be used to gauge the similarity of two documents. The w denotes the number of tokens in each shingle in the set.
The document, "a rose is a rose is a rose" can be tokenized as follows:
(a,rose,is,a,rose,is,a,rose)The set of all contiguous sequences of 4 tokens (4-grams) is
{ (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is), (a,rose,is,a), (rose,is,a,rose) } = { (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is) }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 [0,1], where 1 indicates that two documents are identical. This definition is identical with the Jaccard coefficient describing similarity and diversity of sample sets.