Evolutionary Biological Data Science Laboratory

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, iw_EM can be calculated as:

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

where E_i and n are the i^th element and length of E, respectively.

Example

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

Citations (Ci)	47	26	19	15	11	10	4	3	2	1	1	1	1	0	0	0	0	0
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
						E1 = 6
Adjusted Citations (Ci)	41	20	13	9	5	4
Rank (i)	1	2	3	4	5	6
					E2 = 5
Adjusted Citations (Ci)	36	15	8	4	0
Rank (i)	1	2	3	4	5
				E3 = 4
Adjusted Citations (Ci)	32	11	4	0
Rank (i)	1	2	3	4
			E4 = 3
Adjusted Citations (Ci)	29	8	1
Rank (i)	1	2	3
		E5 = 2
Adjusted Citations (Ci)	27	6
Rank (i)	1	2
		E6 = 2
Adjusted Citations (Ci)	25	4
Rank (i)	1	2
		E7 = 2
Adjusted Citations (Ci)	23	2
Rank (i)	1	2
		E8 = 2

iw_EM is the sum of each component of E weighted by it's order, thus iw_EM = 6/1 + 5/2 + 4/3 + 3/4 + 2/5 + 2/6 + 2/7 + 2/8 = 11.8524

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