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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 (geometric credit), except that it estimates its own core rather than relying on the standard h-index 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)591126161110343111200000
Authors (Ai)313234144112442111
Author Position (ai)113213113111331111
Author Effort (Ei)0.571.000.140.330.570.131.000.530.131.001.000.670.130.130.671.001.001.00
Weight (wi)1.751.007.003.001.757.501.001.887.501.001.001.507.507.501.501.001.001.00
Adjusted Citations (\(C^*_i\))44.6011.009.839.248.323.653.002.921.101.001.000.820.730.000.000.000.000.00
Rank (i)123456789101112131415161718
he = 5

The largest rank where \(i \leq C^*_i\) is 5. Interpolating between this and the next largest rank yields hap.geom = 5.5853.

History

Yearhap.geom
19970.0000
19981.9412
19992.9626
20004.5433
20015.5853
20026.8571
20038.4000
200411.2500
200513.2280
200614.2911
200717.4906
200820.0000
200921.6713
201024.0000
201125.4487
201227.4031
201328.5934
201429.0648
201529.7039
201630.0237
201730.8491
201831.8559
201932.1208
202033.7667
202135.5516
202236.8146
202336.8658
202437.5622
202537.7379

References