A geometric approach to the construction of scientific impact indices

  title={A geometric approach to the construction of scientific impact indices},
  author={Marek Gagolewski and Przemyslaw Grzegorzewski},
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… 
Analysis of the Hirsch index's operational properties
An axiomatic approach to bibliometric rankings and indices
Possible and Necessary h-Indices
A class of so-called p-sphere indices, which generalize the well known Hirsch index, is used to construct a possibility measure of scientific impact, which might be treated as a starting point for prediction of future index values or for dealing with right-censored bibliometric data.
The fractal dimension of a citation curve: quantifying an individual’s scientific output using the geometry of the entire curve
The concept of fractal dimension is introduced to further examine the citation curve of an author to provide insight in its shape and form, level of skewness and distance from uniformity as well as the existing publishing patterns, without a priori assumptions on the particular citation distribution.
Scientometric Indices Based on Integrals and Their Adaptation in Different Domains
A new Sugeno integral - based representation of h-index is proposed and a proposal based on modification of considered monotone measures allowing to compensate differences between particular scientific domains is presented and discussed.
Bibliometric impact assessment with R and the CITAN package
Weighting Factor Mechanism of Uncited Papers to Improve the Fairness of RA-index based on Particle Swarm Optimization
Particle swarm optimization (PSO) method is used to optimize the weighting of the uncited papers and the number of citations below the H-index value (lower-h-tail area) and results showed that the RA-Index is fairer than its competitors.


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
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
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
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
  • 2006
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?
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
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.