Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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adapted pure h-index (proportional 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 proportional (artihmetic) assignment of credit for each publication as:

$$E_i=\frac{2\left(A_i + 1 - a_i\right)}{A_i\left(A_i + 1\right)},$$

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

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

Example

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

Citations (Ci)42369111492232111000
Authors (Ai)3312341144124421
Author Position (ai)1112331131113311
Author Effort (Ei)0.500.501.000.330.170.201.001.000.200.401.000.670.200.200.671.00
Weight (wi)2.002.001.003.006.005.001.001.005.002.501.001.505.005.001.501.00
Adjusted Citations (\(C^*_i\))29.7025.469.006.355.724.022.002.001.341.261.000.820.450.000.000.00
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.prop = 5.2659.

History

Yearhap.prop
19970.0000
19981.9237
19992.6470
20004.0548
20015.2659
20026.6840
20038.1439
20049.9153
200511.5293
200613.4613
200715.3925
200817.5954
200919.7703
201021.1863
201123.0000
201224.0000
201325.7231
201427.7128
201528.2902
201630.2195
201730.3556

References