A set of functions which take two sets or bag of words and measure their similarity or dissimilarity.

Usage

jaccard_similarity(a, b)

jaccard_dissimilarity(a, b)

jaccard_bag_similarity(a, b)

ratio_of_matches(a, b)

Arguments

a

The first set (or bag) to be compared. The origin bag for directional comparisons.

b

The second set (or bag) to be compared. The destination bag for directional comparisons.

Details

The functions jaccard_similarity and jaccard_dissimilarity provide the Jaccard measures of similarity or dissimilarity for two sets. The coefficients will be numbers between 0 and 1. For the similarity coefficient, the higher the number the more similar the two sets are. When applied to two documents of class TextReuseTextDocument, the hashes in those documents are compared. But this function can be passed objects of any class accepted by the set functions in base R. So it is possible, for instance, to pass this function two character vectors comprised of word, line, sentence, or paragraph tokens, or those character vectors hashed as integers.

The Jaccard similarity coeffecient is defined as follows:

$$J(A, B) = \frac{ | A \cap B | }{ | A \cup B | }$$

The Jaccard dissimilarity is simply

$$1 - J(A, B)$$

The function jaccard_bag_similarity treats a and b as bags rather than sets, so that the result is a fraction where the numerator is the sum of each matching element counted the minimum number of times it appears in each bag, and the denominator is the sum of the lengths of both bags. The maximum value for the Jaccard bag similarity is 0.5.

The function ratio_of_matches finds the ratio between the number of items in b that are also in a and the total number of items in b. Note that this similarity measure is directional: it measures how much b borrows from a, but says nothing about how much of a borrows from b.

References

Jure Leskovec, Anand Rajaraman, and Jeff Ullman, Mining of Massive Datasets (Cambridge University Press, 2011).

Examples

jaccard_similarity(1:6, 3:10)
#> [1] 0.4
jaccard_dissimilarity(1:6, 3:10)
#> [1] 0.6

a <- c("a", "a", "a", "b")
b <- c("a", "a", "b", "b", "c")
jaccard_similarity(a, b)
#> [1] 0.6666667
jaccard_bag_similarity(a, b)
#> [1] 0.3333333
ratio_of_matches(a, b)
#> [1] 0.8
ratio_of_matches(b, a)
#> [1] 1

ny         <- system.file("extdata/legal/ny1850-match.txt", package = "textreuse")
ca_match   <- system.file("extdata/legal/ca1851-match.txt", package = "textreuse")
ca_nomatch <- system.file("extdata/legal/ca1851-nomatch.txt", package = "textreuse")

ny         <- TextReuseTextDocument(file = ny,
meta = list(id = "ny"))
ca_match   <- TextReuseTextDocument(file = ca_match,
meta = list(id = "ca_match"))
ca_nomatch <- TextReuseTextDocument(file = ca_nomatch,
meta = list(id = "ca_nomatch"))

# These two should have higher similarity scores
jaccard_similarity(ny, ca_match)
#> [1] 0.5347534
ratio_of_matches(ny, ca_match)
#> [1] 0.7372765

# These two should have lower similarity scores
jaccard_similarity(ny, ca_nomatch)
#> [1] 0.003307607
ratio_of_matches(ny, ca_nomatch)
#> [1] 0.01395349