Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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adapted pure h-index (geometric credit)

The adapted pure h-index (Chai et al. 2008) is very similar to the pure h-index, except that it estimates its own core rather than relying on the standard Hirsch core. For a given publication, if one has information on author order and assumes the order directly correlates with effort, one can use a geometric assignment of credit for each publication as:

$$E_i=\frac{2^{A_i - a_i}}{2^{A_i} - 1},$$

where ai is the position of the target author within the full author list of publication i (i.e., an integer from 1 to Ai). Each publication can then be weighted by the inverse of the author effort, wi = 1/Ei. The effective number of citations for each publication is then calculated as

$$C^{*}_i = \frac{C_i}{\sqrt{w_i}}.$$

Publications are ranked according to these new citation counts and the h-equivalent value, he, is found as the largest rank for which the rank is less than the number of equivalent citations, or

$$h_e = \underset{i}{\max}\left(i \leq C^{*}_i\right).$$The adapted pure h-index is calculated by interpolating between this value and the next largest, as

$$h_{ap.\text{geom}}= \frac{\left(h_e+1\right)C^{*}_{h_e}-h_e C^{*}_{h_e +1}}{C^{*}_{h_e}-C^{*}_{h_e+1}+1}.$$

Example

Publications are ordered by adjusted number of citations, from highest to lowest.

Citations (Ci)42369111492223111000
Authors (Ai)3312341144124421
Author Position (ai)1112331113113311
Author Effort (Ei)0.570.571.000.330.140.131.001.000.530.131.000.670.130.130.671.00
Weight (wi)1.751.751.003.007.007.501.001.001.887.501.001.507.507.501.501.00
Adjusted Citations (\(C^*_i\))31.7527.219.006.355.293.292.002.001.461.101.000.820.370.000.000.00
Rank (i)12345678910111213141516
he = 5

The largest rank where \(i \leq C^*_i\) is 5. Interpolating between this and the next largest rank yields hap.geom = 5.0970.

History

Yearhap.geom
19970.0000
19981.9296
19992.5972
20003.8802
20015.0970
20026.6093
20038.1417
20049.8748
200511.5293
200613.0000
200714.6385
200817.1381
200919.3865
201021.0000
201122.0149
201223.7526
201325.2558
201426.7072
201526.7635
201627.5221
201727.5221

References