Towards a typology of research performance diversity: the case of top Hungarian players

Abstract

Measuring the intellectual diversity encoded in publication records as a proxy to the degree of interdisciplinarity has recently received considerable attention in the science mapping community. The present paper draws upon the use of the Stirling index as a diversity measure applied to a network model (customized science map) of research profiles, proposed by several authors. A modified version of the index is used and compared with the previous versions on a sample data set in order to rank top Hungarian research organizations (HROs) according to their research performance diversity. Results, unexpected in several respects, show that the modified index is a candidate for measuring the degree of polarization of a research profile. The study also points towards a possible typology of publication portfolios that instantiate different types of diversity.

Appendix

See Tables 2, 3; Fig 4.

Table 2 The list of major Hungarian Research Institutions (HROs)

Table 3 Values obtained from applying the two versions of the Stirling index on the sample of HROs: div_sim and div_wpath stands for the cosine distance version and the weighted path length version, respectively

Fig. 4

Distribution of shortest path lengths for the map of science used as basemap (left: unweighted path lengths measured by the number of edges, right: weighted path lengths measured by the sum of edge weights)

Conceptual relations of the distance measures of the proposed and the popular versions of the Stirling index

The relation between the proposed distance measure, the weighted path length $g_{ij}^{W}$, and the popular distance measure, the cosine distance is illustrated by Fig. 5. On the graph, a configuration of SCs characteristic of the basemap is depicted: SCJ can be reached from SCI in two steps, and vice versa, as these are connected by SCK. The dotted line stands for an edge that is either nonexistent or omitted, bearing a weight below the chosen minimum of similarity values. On the lines edge weights are indicated.

Fig. 5

The configuration of three SCs in the science map

In this case, the two calculations would provide the following results.

• (1) Cosine distance Applying the cosine distance as the distance parameter means using directly the edge weights in the Stirling index. In the case shown below, the distance between SC _I and SC _J is

  $$ { \cos }\left({\mathbf{SC}}_{I} ,{{\mathbf{SC}}_{J} } \right) = {\mathbf{d}}_{IJ} $$

• (2) Weighted path length By our definition, the distance between SC _I and SC _J is the weighted (shortest) path length, which, assuming that the direct link between the two is omitted, yields

  $$ g^{W} \left( {{\mathbf{SC}}_{I} ,{\mathbf{SC}}_{J} } \right) = {\mathbf{d}}_{KI} + {\mathbf{d}}_{KJ}. $$

Since the direct link connecting the two SCs is missing, the cosine similarity between them is zero (or set to zero by imposing the threshold), by which the cosine distance (1–cosine similarity) equals to 1. The sum of the other two weights could be either above, or below this value, since the cosine distance does not obey to the rule of triangle inequality (Korenius et al. 2007), by which fact

$$ {\mathbf{d}}_{KI} + {\mathbf{d}}_{KJ} \ge {\mathbf{d}}_{IJ} $$

does not hold, therefore

$$ { \cos }\left({{\mathbf{SC}}_{I} ,{\mathbf{SC}}_{J} } \right) \le \ge g^{W} \left( {{\mathbf{SC}}_{I} ,{\mathbf{SC}}_{J} } \right) $$

For the diversity measure, these considerations have the consequence that using the weighted path length measure can make the diversity index much more sensible to the relatedness of Subject Categories in that it approximates otherwise uniformly treated distances (missing links) by different values. Theoretically, this also holds for the case where no threshold is used, and the calculation depends on the full weight matrix of the network, which means placing back some links to the system. Set aside the remaining set of missing links (the representing SCs not related at all), the path length values might also differ from cosine similarity values for below-threshold connected SCs as well, mirroring a different kind of connection between them.