# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## trend h-index

The trend h-index (Sidiropoulos et al. 2007) is essentially the opposite of the contemporary h-index. It is designed to measure how current an author's impact is by how recently they are being cited. The trend score for a publication is measured as

$$S^t_i = \gamma \sum\limits_{j=1}^{C_i}{\left(Y-Y_{j.i}+1\right)^{-\delta}}$$

where γ and δ are parameters (often set to 4 and 1, respectively, just as with the contemporary h-index) and Yj.i is the year of the jth citation for publication i. If the number of citations for publication i in year Yk is Ci.k, this can also be written as $$S^t_i = \gamma \sum\limits_{k=1}^{Y}{C_{i.k}\left(Y-Y_k+1\right)^{-\delta}}.$$The trend h-index is the largest value for which an author has ht publications with at least Stht.

$$h^t = \underset{i}{\max}\left(i \leq S^t_i\right)$$

### Example

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

 Citations (Ci) —1997— —1998— —1999— —2000— —2001— Adjusted Citations ($$S^{t}_i$$) Rank (i) 36 42 14 11 9 9 2 2 3 2 1 1 1 0 0 0 — 1 0 — 0 0 — — 1 — — — — — — — — 5 2 3 1 0 — — 0 — — — — — — — — 13 6 1 1 2 — — 0 0 — — — — — — 5 8 2 4 3 6 0 — 1 2 0 0 — 0 — — 31 15 4 3 4 1 2 2 1 0 1 1 1 0 0 0 134.00 99.13 30.00 24.33 24.33 18.67 8.00 8.00 6.80 4.00 4.00 4.00 4.00 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 hC = 8

The largest rank where $$i \leq S^{t}_i$$ is 8.

Yearht
19972
19984
19995
20007
20018
200212
200314
200417
200517
200620
200723
200824
200925
201029
201129
201232
201333
201433
201532
201629
201729

## References

• Sidiropoulos, A., D. Katsaros, and Y. Manolopoulos (2007) Generalized Hirsch h-index for disclosing latent facts in citation networks. Scientometrics 72(2):253–280.