w-shingling

In natural language processing a w-shingling is a set of unique "shingles"—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 (N-grams, here: 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

$r(A,B)={{|S(A)\cap S(B)|}\over {|S(A)\cup S(B)|}}$

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.