Weighted Hir sch index
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Transcript of Weighted Hir sch index
Institute of Information Technology of ANAS
Rahila Hasanova
23.05.2013
"New Challenges in the European Area: International Baku Forum of Young Scientists
A scientist has index h if h of his or her Np papers have at least h citations each and the other (Np – h) papers have ≤h citations each.
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first h papers
More than h citations
Papers
citations= papers= h
J.E.Hirsch, An index to quantify an individual’s scientific research output // Proceedings of the National Academy of Sciences of the USA, 2005, vol.102, no.46, pp.16569-16572.
Quantity (publications) and impact (citations). Awarding prizes Single-number criteria Easy to understand
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Differences among fields. Scientist's career.. Citation to journal articles… Decrease…. Highly cited papers….. Self-citations…..
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Solomon H. Snyder: h = 191
Hector Garcia-Molina: h = 88
Suppose that, the scientific researcher has 9 papers and these papers received 20, 15, 7, 5, 5, 5, 4, 2, 2 citations accordingly.
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Articles’ rank of the researcher
1 2 3 4 5 6 7 8 9
Number of citations
20 15 7 5 5 5 4 2 2
Hirsch core
h = 5
The highest rank such that the top g papers have, together, at least g2 citations. This also means that the top g+1 have less than (g+1)2 papers.
Example. Suppose that, the scientific researcher has 9 papers and these papers received 20, 15, 7, 5, 5, 5, 4, 2, 2 citations accordingly.
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Let's compare his h-and g-indices.
Articles’ rank of a researcher
1 2 3 4 5 6 7 8 9
Number of citations
20 15 7 5 5 5 4 2 2
L.Egghe, Theory and practice of the g-index // Scientometrics, 2006, vol.69, no.1, pp.131-152.
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Citations for each paper
The rank of the paper
Sum of citations
The square rank of the
paper
20 1 20 1
15 2 35 4
7 3 42 9
5 4 47 16
5 5 52 25
5 6 57 36
4 7 61 49
2 8 63 64
2 9 65 81
h-core
g-core
h = 5, g = 7
m-index the median number of citations received by papers in the Hirsch core.
Example. Suppose that, the scientific researcher has 8 papers and these papers received 23, 20, 19, 12, 7, 4, 3 and 1 citations accordingly.
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Articles’ rank of the researcher 1 2 3 4 5 6 7 8
Number of citations 23 20 19 12 7 4 3 1
h = 5
m = 19
Papers including to Hirsch core
Q.L.Bornmann, R.Mutz, and H.D.Daniel, Are there better indices for evaluation purposes than the h-index using data from biomedicine // Journal of the American Society for Information Science and Technology, 2008, vol.59, no.5, pp.830-837.
Arithmetic mean
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2
22 mhRhm
Root mean square
Geometric mean
mh
hmHhm
2
Harmonic mean
hmGhm
2
mhAhm
*Aliguliyev, R., Hasanova, R., The evaluation of the scientific output of researchers / The 3rd International Conference “Problems of Cybernetics and Informatics”, 6-8 Sept. 2010, Baku: http://www.pci2010.science.az/1/35.pdf **Jipa S., Gorghiu L.M., Dumitrescu C., Oros C. Research output new evaluation of chemistry group in Valahia university with the use of various bibliometric indicators // Journal of Science and Arts, 2012, no. 3, vol. 20, pp. 335-342. http://www.icstm.ro/DOCS/josa/josa_2012_3/b_06_Silviu_Jipa.pdf
For compare researchers with the same h-index, to the number of citations coming to each paper in Hirsch core, added arithmetic mean of authors’ h-indexes (who cited these researchers’ papers) as weighted coefficient.
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Assume that,
I scientific researcher has 6 papers and these papers received citations accordingly.
II scientific researcher has 6 papers and these papers received 6, 3, 2, 0, 0, 0 citations accordingly.
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For the first researcher h=2
For the second researcher h=2
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Rank I researcher Rank II researcher
1 <5 1 <6
2 <4 * 2 <3 *
3 >2 3 >2
4 >1 4 >1
5 >1 5 >1
6 >0 6 >1
Let’s sort number of citations coming to the papers of both researchers in decreasing order:
*Here the power of citations coming to the papers is not taken account (for ex., h-index of citation’s author, impact factor of the journal from where citation coming and etc.).
For I researcher h=2, g=3, m=4.5
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Number of citations
RankSum of
citationsSquare
rank
5 1 5 1
4 2 9 4
2 3 11 9
1 4 12 16
1 5 13 25
0 6 13 36
Let’s sort number of citations coming to the papers of both researchers in decreasing order :
*Here the power of citations coming to the papers is not taken account (for ex., h-index of citation’s author, impact factor of the journal from where citation coming and etc.).
For II researcher h=2, g=3, m=4.5
Number of citations
RankSum of
citationsSquare
rank
6 1 6 1
3 2 9 4
2 3 11 9
1 4 12 16
1 5 13 25
1 6 14 36
Here,
For the first researcher’s h-index his the first and the second paper gives 1 point each. So,
h(I) = 1 (for number of citations coming to the first paper) + 1 (for number of citations coming to the second paper) = 2
For the second researcher’s h-index his the first and the second paper gives 1 point each. So,
h(II) = 1 (for number of citations coming to the first paper) + 1 (for number of citations coming to the second paper) = 2
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Number of citation of the first paper for I researcher is 5,
number of citations of the second paper is 4.
I paper
I citation
II citation
III citation
IV citation
V citation
II paper
I citation
II citation
III citation
IV citation
*Here number of citations >= 2, that is way they are taken into account.
h=2
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H-index of authors of citations coming to the first paper of I researcher is equal to 4, 3, 2, 0, 0 accordingly.
H-index of authors of citations coming to the second paper of I researcher is equal to 7, 6, 1, 1 accordingly.
I paper
I citation
II citation
III citation
IV citation
V citation
II paper
I citation
II citation
III citation
IV citation
h=4 h=3 h=2
h=0 h=0
h=7 h=6
h=1 h=1
*Here h-index of each citation’s author is taken account. Thus, if any of citations has 2 or more co-authors, then h-index is calculated as arithmetic mean of these authors’ h-index. Self-citation is calculated as h=0.
Normally, the first and the second papers give 1 point each to h-index of the I researcher. Here we include weighted coefficients to these points:
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55.54
11671
5
002341
Ih
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Number of citation of the first paper for II researcher is 6,
number of citations of the second paper is 3.
I paper
I citation
II citation
III citation
IV citation
VI citation
II paper
II citation
III citation
V citation
I citation
*Here number of citations >= 2, that is way they are taken into account.
h=2
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H-index of authors of citations coming to the first paper of II researcher is equal to 6, 6, 1, 1, 0, 0 accordingly.
H-index of authors of citations coming to the second paper of II researcher is equal to 1, 1, 0 accordingly.
I paper
I citation
II citation
III citation
IV citation
VI citation
II paper
II citation
III citation
V citation
I citation
h=6 h=6 h=1
h=1
h=0h=0
h=1
h=1
h=0
*Here h-index of the citation’s author is taken account. Thus, if any of citations has 2 or more co-authors, then h-index is calculated as arithmetic mean of these authors’ h-index. Self-citation is calculated as h=0.
Normally, the first and the second papers give 1 point each to h-index of the II researcher. Here we include weighted coefficients to these points:
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33.33
0111
6
0011661
IIh
*As seems from example, h(I)>h(II). This means that, the power of citations of the I researcher’s papers is higher than the power of citations of the II researcher’ papers.
h(I) = 5.55
h(II) = 3.33
Institute of Information Technology of ANAS
“Weighted Hirsch index”, Rahila Hasanova
23.05.2013