Bibliometric analysis on mathematics
3 snapshots: 2005, 2010, 2015
S. Richard, Q. Sun
Content:I) General pictureII) Individual predictors and the response
III) Best predictor and predictions

Galina LevitinaIV) About countries

Cwikel-type estimates onopen domains

V) Conclusion(Himeji 2022)
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I) General picture
Original question:

What are the important predictors for the publications in mathematics,
if the response is the number of citations ?
Previous works:• Several on different fields, but not centred on mathematics• Grossman (2002, 2005) about research collaboration, with MathSciNet• Bensman et al. (2010) about citation indices for math journals• Behrens and Luksch (2011) bibliometric analysis on the period 1868 - 2008• Özkaya (2018) bibliometric analysis but about math education• Szomszor et al. (2020) Individual perspective about self-citations• Verma et al. (2021) bibliometric analysis over 40 years for a single journal• Dunne (2021) On individual citations, based on MathSciNet• Paik and Rivin (preprint) on US mathematics faculties with some bibliometric tools
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Which database ?

Research area = mathematics

Yearly new indexed math publications

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MathSciNet

Web of SciencePublications with at least one author from a given country,
Absolute and relative numbers

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MathSciNet

Web of ScienceNothingsimilarMore accurate
Centred on mathematics
No automatic downloading
No robot allowed

Less accurate
Mathematics in a broad sense
Massive downloading possible

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Raw data
Research area = mathematics, clear author(s) and affiliation(s), citation < 642005: 42’792 items
Predictors:# authors# institutes# countries# references# pages# keywords
open access (Y/N)
JIFresearch area
category

Response:# citations

2010: 61’084 items

2015: 76’168 items

Simple statistics: mean number / publication
2005

2010

2015

Authors

2.10

2.23

2.39

Institutes

1.57

1.74

1.90

Countries

1.23

1.28

1.32

References (0 excluded)

19.0

21.7

24.5

Pages

15.5

15.5

16.9

Keywords (0 excluded)

4.38

4.48

4.58

Open Access (by WoS)

16.4%

21.2%

32.3%

Citations

10.0

8.5

5.3
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II) Individual predictors and the response# authors:# countries:

Number of citations

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# references:

Logscale

Centred on
the mean:
2005: 10
2010: 8.5
2015: 5.3

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# pages# keywords

Open access

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Journal Impact Factor
Research area = mathematics, clear author(s) and affiliation(s), citation < 64, JIF available

2005: 35’556 items

2010: 44’639 items

2015: 57’756 items
Citation mean:
2005: 12.0
2010: 10.2
2015: 6.3

10/16III) Best predictor and predictions
Tree classifier: 10 predictors, response partitioned in J classes

1) Generate best splits by minimizing an impurity function2) Leaves labeled by majority of class J items
3) Reduce the size of the tree by pruning, best size obtained withtraining set4) Best predictor generates maximal decay of impurity
Predictions: Test new items on the best tree
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The outcome:Free choiceSome predictors

Content mattersmore thanbibliometricdata

Random guess:

20 %

25 %

33 %
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IV) About countries

Relative importance of each country (at least 1 author from a given country)% = percentageof publications
mn = citationmean
md = citation
medianr.c. = relative
citationh.c. = highly cited. Percentage of publications having
more than 63 citations
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International collaborations (at least 2 countries involved)% = percentageof publications
mn = citationmean
md = citation
medianrcc = relative citation for international collaborations. Ratio of mn by the citation
mean over all publications of this country with less than 64 citations
rc2 = relative citations for international collaborations / 2 authors. Ratio of mn by thecitation mean over all publications of this country with less than 64 citations and at
least 2 authors.

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3)

Bilateral collaborations
For a country in x-coordinate,
the numbers correspond to the %of its international collaborations
with a country of the y-coordinate
20052010
2015

15/16V) Conclusion
1) Everything increase2) Predictors can not predict so much3) Good practices are useful4) International collaborations are beneficial
5) MathSciNet should allow such investigations
is useful and should be praised

Thank you
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