Introduction of "Kriging" to Scientometrics for Representing Quality Indicators in Maps of Science

Introduction Maps of science are an effective technique, especially for non-experts, to facilitate intuitive understanding of science activities, even though they could be cut both ways. Among such maps, science overlay maps have received adequate attention from scientometrics researchers (PerianesRodríguez et al., 2011; Grauwin & Jensen, 2011; Klaine et al., 2012; Leydesdorff, Rotlo, & Rafols, 2012; Boyack & Klavans, 2013; Gorjiara & Baldock, 2014). Actually they are an attractive approach “to visually locate bodies of research within the sciences, both at each moment of time and dynamically.” (Rafols, Porter, & Leydesdorff, 2010) To produce science overlay maps, (1) we draw a basemap, which contains positional information of nodes from bibliographical data, then (2) we overlay other information on the basemap by assigning the information (i.e., indicators like publications and citations) to the nodes with such factors as colors and/or size of circles representing the nodes. To think more abstractly, an essence of science overlay maps is “sharing” of positional information of nodes by different science maps, which are similar in concept to thematic maps in geography. What makes such “sharing” possible is the stability of global maps (Rafols, Porter, & Leydesdorff, 2010). This perspective could broaden choices of expressions in science overlay maps to improve our understandings. For example, VOSviewer (Van Eck & Waltman 2010) provides five different views, i.e., label view, density view, scatter view, cluster view, and cluster density view, for a fixed set of positional information of nodes. By switching these views, we can understand phenomena behind the maps deeply and multidimensionally. Therefore, introducing a new way to project bibliographical information on given maps is expected to expand availability of science overlay maps, just as a new method to produce thematic maps does in geography. From this perspective, the author first pays attention to density view provided by VOSviewer. By mapping journals in the fields of Business, Business-Finance, Economics, Management, and Operations Research & Management Science, Van Eck and Waltman (2010, p. 529) explain functionality of the density view as follows: “The density view immediately reveals the general structure of the map. Especially the economics and management areas turn out to be important. These areas are very dense, which indicates that overall the journals in these areas receive a lot of citations.” As they pointed out, this view is helpful to outline the macro structures of maps and to show which areas in the maps are important. Basically, however, density view can be used only for representing quantitative indicators, because “the item density of a point in a map depends both on the number of neighboring items and on the weights of these items.” (p. 533) If citations were used as weights of items, the density map might be seen to show “quality” of areas. Actually, citation densities are only a representation of quantities. That is particularly evident in assuming to represent quality (impact) indicators like proportion of top 10% publications in the density view. Judging from many scientometrics studies rely on density or heat maps (e.g., Pinto, Pulgarin, & Escalona, 2014), it would be reasonable to assume that graphical representations like the density view to represent quality indicators on science maps is very helpful to outline the structures of bibliographical data and to show which areas in maps of science are efficient, superior, or highly shared. Then, this paper introduces “kriging” to scientometrics for representing quality indicators.