Abstract
Two broad classes of scientific impact indices are proposed and their properties - both theoretical and practical — are discussed. These new classes were obtained as a geometric generalization of the well-known tools applied in scientometric, like Hirsch’s h-index, Woeginger’s w-index and the Kosmulski’s Maxprod. It is shown how to apply the suggested indices for estimation of the shape of the citation function or the total number of citations of an individual. Additionally, a new efficient and simple O(log n) algorithm for computing the h-index is given.
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References
J. E. Hirsch, An index to quantify individual’s scientific research output, Proceedings of the National Academy of Sciences, 102(46) (2005) 16569–16572.
P. Ball, Index aims for fail ranking of scientists, Nature, 436 (2005) p. 900.
W. Glänzel, On the opportunities and limitations of the H-index, Science Focus, 1(1) (2006) 10–11.
A. Proń, H. Szatyłowicz, Habilitacja dodaje „skrzyde?”?, Forum Akademickie, 3 (2006) (In Polish).
C. D. Kelly, M. D. Jennions, The h-index and career assessment by numbers, Trends in Ecology and Evolution, 21(4) (2006) 167–170.
L. Bornmann, H. D. Daniel, What do we know about the h-index?, Journal of the American Society for Information Science and Technology, 58(9) (2007) 1381–1385.
M. G. Banks, An extension of the Hirsch index: Indexing scientific topics and compounds, Scientometrics, 69(1) (2006) 161–168.
A. F. J. Van Raan, Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgement for 147 chemistry research groups, Scientometrics, 67(3) (2006) 491–502.
J. E. Hirsch, Does the h-index have predictive power?, Proceedings of the National Academy of Sciences, 104(49) (2007) 19193–19198.
Q. L. Burrell, Hirsch index of Hirsch rate? Some thoughts arising from Liang’s data, Scientometrics, 73(1) (2007) 19–28.
M. Schreiber, A case study of Hirsch index for 26 non-prominent physicists, Ann. Phys., 16(9) (2007) 640–652.
R. Costas, M. Bordons, Is g-index better than h-index? An exploratory study at the individual level, Scientometrics, 77(2) (2008) 267–288.
L. I. Meho, Y. Rogers, Citation counting, citation ranking, and h-index of human-computer interaction researchers: A comparison between Scopus and Web of Science, Journal of the American Society for Information Science and Technology, 59(11) (2008) 1711–1726.
W. Glänzel, On the h-index — A mathematical approach to a new measure of publication activity and citation impact, Scientometrics, 67(2) (2006) 315–321.
A. Basu, A note on the connection between the Hirsch index and the Random Hierarchical model, ISSI Newsletter, 3(2) (2007) 24–27.
Q. L. Burrell, Hirsch’s h-index: A stochastic model, Journal of Informetrics, 1 (2007) 16–25.
R. Rousseau, The influence of missing publications on the Hirsch index, Journal of Informetrics, 1 (2007) 2.7.
L. Egghe, Time-dependent Lotkaian informetrics incorporating growth of sources and items, Mathematical and Computer Modelling, 45(7–8) (2007) 864–872.
G. J. Woeginger, An axiomatic characterization of the Hirsch-index, Mathematical Social Sciences, 56(2) (2008) 224–232.
L. Egghe, An improvement of the h-index: the g-index, ISSI Newsletter, 2(1) (2006) 8–9.
L. Egghe, Theory and practise of the g-index, Scientometrics, 69(1) (2006) 131–152.
M. Kosmulski, A new Hirsch-type index saves time and works equally well as the original h-index, ISSI Newsletter, 2(3) (2006) 4–6.
P. D. Batista, M. G. Campiteli, O. Kinouchi, A. S. Martinez, Is it possible to compare researchers with different scientific interests? Scientometrics, 68(1) (2006) 179–189.
B. Jin, L. Liang, R. Rousseau, L. Egghe, The R- and AR-indices: Complementing the h-index, Chinese Science Bulletin, 52(6) (2007) 855–863.
A. Sidiropoulos, D. Katsaros, Y. Manolopoulos, Generalized h-index for disclosing latent facts in citation networks, Scientometrics, 72(2) (2007) 253–280.
G. J. Woeginger, An axiomatic analysis of Egghe’s g-index, Journal of Informetrics, (2008) In press, doi:10.1016/j.joi.2008.05.002.
M. Kosmulski, MAXPROD — A new index for assessment of the scientific output of an individual, and a comparison with the h-index, Cybermetrics, 11(1) (2007).
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Gągolewski, M., Grzegorzewski, P. A geometric approach to the construction of scientific impact indices. Scientometrics 81, 617–634 (2009). https://doi.org/10.1007/s11192-008-2253-y
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DOI: https://doi.org/10.1007/s11192-008-2253-y