Bibliographic coupling edges, weighted by the idf-weighted cosine (SIM)

The cosine counterpart of coupling_strength(). It is the similarity measure $SIM_{CS}$ of (Shen et al. 2019) , which generalises the coupling angle of coupling_angle() (Sen and Gan 1983) : instead of describing a document by a 0/1 vector over references, it uses a vector whose components are the (square roots of the) idf weights of the references, and takes the cosine of the vectors of two documents. The weight is therefore bounded between 0 and 1.

Usage

coupling_similarity(
  dt,
  source,
  ref,
  weight_threshold = 1,
  output_in_character = TRUE
)

Arguments

dt: A data frame or a data.table of direct citations, one row per link between a citing document and a cited reference. It is not modified.
source: Character scalar. The column of the citing documents: they are the nodes of the coupling network.
ref: Character scalar. The column of the cited references.
weight_threshold: Number. The minimum number of shared references for two documents to be linked (1 by default). It applies to the number of shared references, not to the weight.
output_in_character: Logical. If TRUE (default), the identifiers are also returned as character columns from and to, to build a tidygraph graph more easily.

Value

A data.table with one row per pair of documents sharing at least weight_threshold references: the identifiers in from and to (character if output_in_character = TRUE), the similarity in weight (between 0 and 1), and the original identifiers in Source and Target. Each pair appears once, with Source < Target.

Details

Write $N$ for the number of citing documents in the table, $f_j$ for the number of documents citing reference $j$, and $\mathrm{idf}_j = \log(N / f_j)$. The vector of document $A$ has one component per reference of $A$, equal to $\sqrt{\mathrm{idf}_j}$. The cosine of two such vectors is

$$w_{AB} = \frac{\sum_{j \in R(A) \cap R(B)} \mathrm{idf}_j}{\sqrt{S(A) \, S(B)}}, \qquad S(A) = \sum_{j \in R(A)} \mathrm{idf}_j$$

where $S(A)$ sums the idf of all the references of $A$, shared or not (the squared norm of its vector). The numerator is the numerator of the coupling strength. The weight does not depend on the base of the logarithm (the natural logarithm is used), since the base multiplies numerator and denominator by the same constant.

References cited once have $\mathrm{idf}_j = \log N$, the highest value: they cannot create a tie but they increase $S(A)$, as the references of any other kind. A document whose references are all cited by all the documents has $S = 0$: its ties get a weight of 0.

Computing choices: see coupling_strength() ($N$ counts all the citing documents; duplicates and self-citations are ignored; missing identifiers are dropped with a warning; the table of the user is not modified; a zero-row table is returned, with a warning, if no reference is shared). The same memory remark applies.

Versions up to 0.1.1 returned a different quantity, wrongly computed (see NEWS.md): do not compare with their results.

Why use it in research

It combines the two qualities of the measures it generalises: like the coupling strength, shared rare references count more than shared classics; like the coupling angle, the weight is a cosine, bounded by 1, and a long bibliography is normalised away. Use it when you want weights with the same scale as the coupling angle (for instance to apply the same threshold or community detection settings) while discounting the references that all the corpus cites. (Shen et al. 2019) find that, on a corpus of library and information science articles, this similarity is very strongly correlated with the plain coupling angle (a Pearson correlation of 0.996) and somewhat less with the coupling strength (0.887): check on your own corpus, with correlate_weights(), whether it changes anything.

Intuition

Start from the picture of coupling_strength(): the surprise of a shared reference is $\log(N/f)$. Now give every reference of a document an importance equal to its surprise: a bibliography of ten classics carries little information, a bibliography of ten obscure papers carries much. The informational size $S(A)$ of a document is the total surprise of its bibliography, and the similarity compares the surprise that two documents share with their informational sizes, like a cosine. Two documents with short but distinctive bibliographies can be very similar, while two documents with long bibliographies of classics cannot.

References

Sen SK, Gan SK (1983). “A Mathematical Extension of the Idea of Bibliographic Coupling and Its Applications.” Annals of library science and documentation, 30(2).

Shen S, Zhu D, Rousseau R, Su X, Wang D (2019). “A Refined Method for Computing Bibliographic Coupling Strengths.” Journal of Informetrics, 13(2), 605–615. https://linkinghub.elsevier.com/retrieve/pii/S1751157716300244.

Examples

library(biblionetwork)
coupling_similarity(Ref_stagflation,
                    source = "Citing_ItemID_Ref",
                    ref = "ItemID_Ref")
#>             from         to     weight     Source     Target
#>           <char>     <char>      <num>      <int>      <int>
#>    1:    1021902    1184127 0.02944587    1021902    1184127
#>    2:     214927    2207578 0.12438825     214927    2207578
#>    3:    1184127    2901822 0.03451922    1184127    2901822
#>    4:    1184130    2901822 0.04213543    1184130    2901822
#>    5:    1717556    2901822 0.01910916    1717556    2901822
#>   ---                                                       
#> 2712: 1111111122 1111111183 0.03786992 1111111122 1111111183
#> 2713: 1111111134 1111111183 0.03197678 1111111134 1111111183
#> 2714: 1111111146 1111111183 0.03751466 1111111146 1111111183
#> 2715: 1111111161 1111111183 0.02909475 1111111161 1111111183
#> 2716: 1111111182 1111111183 0.24285542 1111111182 1111111183

# Toy example: for d3 and d4, N = 4, the shared reference r4 is cited by
# 2 documents, and S(d3) = 2 log(2), S(d4) = log(2) + log(4), so
# w = log(2) / sqrt(2 log(2) * 3 log(2))
toy <- data.frame(doc = c("d1", "d1", "d1", "d2", "d2", "d3", "d3", "d4", "d4"),
                  ref = c("r1", "r2", "r3", "r1", "r2", "r3", "r4", "r4", "r5"))
coupling_similarity(toy, source = "doc", ref = "ref")
#>      from     to    weight Source Target
#>    <char> <char>     <num> <char> <char>
#> 1:     d1     d2 0.8164966     d1     d2
#> 2:     d1     d3 0.4082483     d1     d3
#> 3:     d3     d4 0.4082483     d3     d4