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)	57	26	16	12	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)	51	20	10	6	5	4
Rank (i)	1	2	3	4	5	6
					E2 = 5
Adjusted Citations (Ci)	46	15	5	1	0
Rank (i)	1	2	3	4	5
			E3 = 3
Adjusted Citations (Ci)	43	12	2
Rank (i)	1	2	3
		E4 = 2
Adjusted Citations (Ci)	41	10
Rank (i)	1	2
		E5 = 2
Adjusted Citations (Ci)	39	8
Rank (i)	1	2
		E6 = 2
Adjusted Citations (Ci)	37	6
Rank (i)	1	2
		E7 = 2
Adjusted Citations (Ci)	35	4
Rank (i)	1	2
		E8 = 2
Adjusted Citations (Ci)	33	2
Rank (i)	1	2
		E9 = 2

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

History