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iterative weighted EM-index

The iterative weighted EM-index (Bihari et al. 2021) is a modification of the EM-index which uses a weighted-sum of each successive element in the vector rather than the square-root of the sum. The index begins by creating a vector (E) which is equivalent to the upper/excess half of the two-sided h-index, namely a series of h-index values calculated from the citation curve of just the core publications, stopping when one reaches only a single remaining publication, no citations remain, or all remaining publications have only a single citation. From this vector, iwEM can be calculated as:

$$iw_{EM}=\sum\limits_{i=1}^{n}\frac{E_i}{i},$$

where Ei and n are the ith element and length of E, respectively.

Example

Publications are ordered by number of citations, from highest to lowest. After each step, Ei is subtracted from the citations of the top Ei publications. All publications beyond the top Ei are ignored at subsequent steps.

Citations (Ci)592616111110433211100000
Rank (i)123456789101112131415161718
E1 = 6
Adjusted Citations (Ci)532010554
Rank (i)123456
E2 = 5
Adjusted Citations (Ci)4815500
Rank (i)12345
E3 = 3
Adjusted Citations (Ci)45122
Rank (i)123
E4 = 2
Adjusted Citations (Ci)4310
Rank (i)12
E5 = 2
Adjusted Citations (Ci)418
Rank (i)12
E6 = 2
Adjusted Citations (Ci)396
Rank (i)12
E7 = 2
Adjusted Citations (Ci)374
Rank (i)12
E8 = 2
Adjusted Citations (Ci)352
Rank (i)12
E9 = 2

iwEM is the sum of each component of E weighted by it's order, thus iwEM = 6/1 + 5/2 + 3/3 + 2/4 + 2/5 + 2/6 + 2/7 + 2/8 + 2/9 = 11.4913

History

YeariwEM
19971.0000
19983.0000
19995.9000
20008.7333
200111.4913
200214.6579
200318.8154
200424.9145
200531.3697
200636.0918
200742.4303
200848.3652
200954.7489
201058.7263
201164.9946
201271.9806
201377.0317
201480.9356
201583.8775
201686.4657
201790.3947
201892.8083
201995.5877
202098.8267
2021101.4538
2022104.9912
2023106.3117
2024109.2584
2025111.6299

References