multidimensional h-index
The multidimensional h-index (García-Pérez 2009) is a simple expansion of the original h-index used to separate individuals with identical h-indices. The concept is to calculate the h-index from all P publications (this would be the first h-index or h1). One can then calculate a second h-index, h2, from the P – h1 remaining publications. Graphically, this is finding the largest square which can fit in the tail to the right of the original square represented by h1. A third, h3, can be calculated from the P – h1 – h2 remaining publications, etc., continuing until one reaches publications with 0 citations.
It should be obvious that h1 ≥ h2 ≥ h3…
Unlike most of the other indices, this index set is primarily focused on the tail of the distribution, ignoring the excess/upper part of the citation curve completely. Because it is simply recalculating h for a smaller data set, its interpretation is quite straightforward and certainly could serve as a solid method of distinguishing individuals with identical h.
Example
Publications are ordered by number of citations, from highest to lowest. Publications determined to be part of a core are removed for subsequent calcluations.
| 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 |
| h1 = 6 | ||||||||||||||||||
| Citations (Ci) | 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 | ||||||
| h2 = 2 | ||||||||||||||||||
| Citations (Ci) | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | ||||||||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||||||
| h3 = 1 | ||||||||||||||||||
| Citations (Ci) | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||||||||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||||||||
| h4 = 1 | ||||||||||||||||||
| Citations (Ci) | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | ||||||||||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||||||||||
| h5 = 1 | ||||||||||||||||||
| Citations (Ci) | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||||||||||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||||||||||
| h6 = 1 | ||||||||||||||||||
| Citations (Ci) | 1 | 0 | 0 | 0 | 0 | 0 | ||||||||||||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | ||||||||||||
| h7 = 1 |
History
| Year | H |
|---|---|
| 1997 | [1, 1] |
| 1998 | [3, 1, 1] |
| 1999 | [3, 2, 1, 1] |
| 2000 | [5, 3] |
| 2001 | [6, 2, 1, 1, 1, 1, 1] |
| 2002 | [7, 4, 3, 2, 1, 1] |
| 2003 | [10, 5, 3, 2, 1] |
| 2004 | [12, 7, 3, 1, 1] |
| 2005 | [14, 7, 3, 2, 1, 1, 1] |
| 2006 | [16, 8, 4, 3] |
| 2007 | [19, 8, 3, 2] |
| 2008 | [21, 10, 2, 2] |
| 2009 | [24, 7, 3, 1, 1, 1] |
| 2010 | [25, 9, 5, 1, 1, 1, 1, 1] |
| 2011 | [28, 10, 4, 2, 1, 1] |
| 2012 | [32, 7, 4, 2, 2, 1, 1] |
| 2013 | [33, 7, 5, 2, 1, 1, 1, 1] |
| 2014 | [34, 8, 5, 3, 2, 1, 1, 1, 1, 1] |
| 2015 | [35, 9, 5, 3, 2, 2, 2, 1] |
| 2016 | [35, 10, 6, 3, 2, 2, 1, 1, 1] |
| 2017 | [37, 11, 5, 3, 2, 2, 1, 1] |
| 2018 | [37, 12, 5, 4, 2, 2, 1, 1, 1] |
| 2019 | [37, 13, 5, 4, 2, 2, 2, 1, 1] |
| 2020 | [38, 13, 6, 4, 3, 2, 2] |
| 2021 | [39, 14, 6, 4, 3, 2, 2] |
| 2022 | [41, 14, 6, 4, 3, 2, 1, 1] |
| 2023 | [42, 14, 6, 5, 3, 2, 2] |
| 2024 | [42, 16, 6, 5, 3, 2, 2, 1, 1] |
References
- García-Pérez, M.A. (2009) A multidimensional extension to Hirsch's h-index. Scientometrics 81(3):779–785.