A geometric approach to the construction of scientific impact indices

@article{Gagolewski2008AGA,
  title={A geometric approach to the construction of scientific impact indices},
  author={Marek Gagolewski and Przemyslaw Grzegorzewski},
  journal={Scientometrics},
  year={2008},
  volume={81},
  pages={617-634}
}
Two broad classes of scientific impact indices are proposed and their properties - both theoretical and practical — are discussed. These new classes were obtained as a geometric generalization of the well-known tools applied in scientometric, like Hirsch’s h-index, Woeginger’s w-index and the Kosmulski’s Maxprod. It is shown how to apply the suggested indices for estimation of the shape of the citation function or the total number of citations of an individual. Additionally, a new efficient and… 
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References

SHOWING 1-10 OF 37 REFERENCES
A case study of the Hirsch index for 26 non‐prominent physicists
The h index was introduced by Hirsch to quantify an individual's scientific research output. It has been widely used in different fields to show the relevance of the research work of prominent
An improvement of the h-index: the g-index
For a set of papers, ranked in decreasing order of the number of citations that they received, the h-index is the (unique) highest number of papers that received h or more citations. In the
Theory and practise of the g-index
TLDR
It is shown that the g-index inherits all the good properties of the h-index and better takes into account the citation scores of the top articles and yields a better distinction between and order of the scientists from the point of view of visibility.
MAXPROD - A New Index for assessment of the scientific output of an individual, and a comparison with the h-index
A new index termed Maxprod is defined as the highest value in the set of ixci where ci is the number of citations of the i-th most cited paper of an individual. For most chemists who have published
Generalized h-index for Disclosing Latent Facts in Citation Networks
TLDR
Several inefficiencies of the h-index are demonstrated and a pair of generalizations and effective variants of it are developed to deal with scientist ranking and with publication forum ranking.
Generalized Hirsch h-index for disclosing latent facts in citation networks
TLDR
The effectiveness and the benefits of the new indices are exhibited to unfold the full potential of the h-index, with extensive experimental results obtained from the DBLP, a widely known on-line digital library.
An extension of the Hirsch index: Indexing scientific topics and compounds
  • M. Banks
  • Computer Science
    Scientometrics
  • 2006
TLDR
This quick method is shown to help new comers to identify how much interest and work has already been achieved in their chosen area of research by comparing both the hb index and m for a number of compounds and topics.
An axiomatic characterization of the Hirsch-index
Is it possible to compare researchers with different scientific interests?
TLDR
This work has obtained the rank plots of h and h I for four Brazilian scientific communities and found the h I index rank plots collapse into a single curve allowing comparison among different research areas.
The R- and AR-indices: Complementing the h-index
TLDR
The R- and AR-indices are introduced and it is proposed the pair (h, AR) as a meaningful indicator for research evaluation and a relation characterizing the h-index in the power law model is proved.
...
...