W-shingling

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) }

By removing duplicate elements from this set, a 4-shingling is obtained:

{ (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

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

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.

See also

• Concept Mining offers an alternative method for document similarity calculation with more computational complexity, but where the measure more closely models a human\'s perception of document similarity.

References

• (Manber 1993) Finding Similar Files in a Large File System. Does not yet use the term "shingling". Available as PDF
• (Broder, Glassman, Manasse, and Zweig 1997) Syntactic Clustering of the Web. SRC Technical Note #1997-015. Available as HTML

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