Interdisciplinarity is a fashion direction in modern education and science. Inter-disciplinarity is impossible without interactions between research from various fields. For quantitative assessment of level of interdisciplinarity, of level different research fields interactions a lot of approaches are proposed in recent years.
Currently the most widely used approaches to quantitative measuring of interdisciplinarity use bibliometrics. They take into account co-authorships, collaborations, references, citations and cocitations. The most common bibliometric technique for measuring inderdisciplinarity is some kind of citation analysis. A citation environment is defined as all journals that cite or are cited by a specific journal [1].
In [2] authors measure interdisciplinarity by relating papers' cited journals to their corresponding subject categories of Web of Science. Their metrics take into account the inter-relatedness of subject categories. They use the following quantities deducted from citation of papers of a single subject category: number of papers published in journals associated with this subject category; number of cites by these papers to papers in journals associated with this subject category; number of cites to these papers by papers in journal associated with this subject category.
Another approach based on citations is presented in [3]. It shows that the fraction of paper references that point to work in other disciplines is increasing in both the natural and the social sciences and the fraction that points to another specialty in the same discipline has a slight decline. The measures are done using varietythe spread of references across disciplines and disparity -the "intellectual distance" between disciplines in references. The key results they concluded is that interdisciplinarity research takes time to have an impact and that some fields as well as countries are more interdisciplinary than others.
A slightly less used approach for measuring interdisciplinarity using bibliometric uses collaborations. In [4] authors used graph of collaboration between researches to investigate the interdisciplinarity of scientific fields. They estimate similarity between science categories using text similarity between their descriptions. Their measure of interdisciplinarity is based on Stirling's diversity index.
Some of the studies use text analysis to quantify the interaction and evolution of scientific disciplines. In [5] authors compare different measures of dissimilarity between scientific fields. These measures are based on expert classification, citations and information theory.
All the above mentioned approaches require large information resources. Methods that based on citation analysis, are pretty inertial. It is impossible to assess interdisciplinarity of a new paper instantly, because citations take time to take place. As opposed to the mentioned approaches, paper [6] proposed a new technique to assess the similarity between research fields. The technique applies to information resources of Dimensions with already categorized research papers. Dimensions was launched in 2018 and many researchers started using it immediately for bibliometric research [7,8,9,10]. Dimensions uses hierarchical system of research classification, included divisions at high level and research group at low level. In paper [6] similarity of research groups is assessing via Jaccard index.
The current paper extends idea of [6] in the following directions: 1) assessing the research interactions at the high levelat level of divisions; 2) assessing the interdisciplinarity at the low level taking into account only interactions with research groups from different divisions according to arguments of [11] about various impacts for interdisciplinarity levels for various combinations of research fields; 3) improving the research classifying system on base of actual statistics of research fields interactions. Analysis of the research interactions is carried for 4 five-year periods on base of papers dated 2001-2020. Dimensions has indexed over 110M research papers. Each paper is assigned to one or several research groups. Such categorization is carried out in by Dimensions itself by special software based on machine learning guided by topic experts [12]. As training data Dimensions uses title and abstract of the paper for this categorization.
Based on Dimensions data we can retrieve a number of papers assigned to each research division. At the same time, we can get the number of above-mentioned papers that were assigned to several research divisions simultaneously. By using this information we assess the interaction of any pair of research divisions using 2 queries. According to [6] we use Jaccard index for assessing the interactions of two research divisions A and B as follows: . Jaccard index distributions for two research divisions within the four of the five-year periods are shown in Figure 1. The x-axis corresponds to ranked list of pairs of divisions sorted ascending for each period separately. The y-axis corresponds to their level of interaction plotted in log scale. Overall, we analyzed 231 pairs of divisions. Figure 1 shows that every consecutive five-year period has decreased irregularity of its distribution of interaction. We can see that by observing that pairs of divisions from the beginning of Jaccard index distribution has their interaction decreased over time and the pairs at the end of the distribution on the contraryincreased. This observation is confirmed by Gini coefficient that decreases in time in the following way: In addition to paired interaction, we analyzed the cumulative interaction of divisions. For this stickiness index [5] Figure 4 shows that all research divisions tend to have their stickiness decreased over time. This conclusion is confirmed by Gini index for stickiness distributions that decreases from 0.197 in the first period to 0.188 in the last period. For all time of observations, the most rapid decrease in stickiness index is demonstrated by the following research divisions:
22 Philosophy and Religious Studies --34%;
In addition to research divisions based on Dimensions data we can retrieve a number of papers assigned with each research group. At the same time, we can get a number of above-mentioned papers that were assigned to several research groups simultaneously. By using this data, we can assess the level of interaction between two research groups in the same way as for divisions. For example, there are 80115 papers assigned to group 0806 Information Systems in 2019, and 2934 of them also belong to group 1503 Business and Management. Group 1503 consist of 59662 papers published in 2019.
Figure 5 shows the Jaccard index distributions for pairs of research groups with different divisions within the four of the five-year periods. We empirically set a threshold for a number of papers for a research division to be 1000, so that research divisions with less than 1000 papers are not considered. In total 145 research groups are considered, hence the interactive level of 10440 pairs of the research groups for each five-year period were calculated. Most of the research groups have zero Jaccard index. Figure 4 shows the same results as with the research divisions' interactions. But now the pairs at the end of the distribution have their interactions increased by a larger factor which shows that as the time goes on interdisciplinarity between research divisions increases. This can be seen by looking at Figure 5 and observing that the first period 2001-2005 has 334 pairs of research divisions with Jaccard index greater than zero. The last period has 551 pairs, which give an increase of 217 pairs over the last 2 decades. The same effect shows Gini coefficient that decreases in time in the following way: Figure 6 shows the dynamic of the interaction for the most tied groups. We apply the same selection here as for the divisions. For the all four periods, we observe the following 3 leaders that always stay in the top 5:
1205 Urban and Some of the leaders increase interaction as time goes on, some decrease interaction, some switch between increasing and decreasing interaction. A trend towards increasing interaction shows 0502 Environmental Science and Management & 0602 Ecology. This pair increases the interaction from 0.11 in the first period to 0.16 in the last period. A trend towards decreasing interaction show a few pairs of groups: 1205 Urban As well as with research divisions, we analyzed the cumulative interaction of groups. We used the same formula of stickiness index but, naturally, applied to Jaccard indexes of research groups. The distributions of stickiness indexes for each of the periods are shown in Figure 8. The leaders by stickiness index are:
0502 Environmental Science and Management; 2001 Communication and Media Studies; 1205 Urban and Regional Planning. Figure 8 confirms to the previous conclusion regarding to divisions and shows that with time research groups tend to have a more equally distributed stickiness index. It is also observed from the number of research groups that increased their stickiness index from zero to greater than zero. 11 research groups have increased their stickiness index from zero in the first period to positive number in the last period, and only one research group has decreased it to zero. The same effect shows Gini index for the stickiness index that decreases from 0.4722 in the first period to 0.4519 in the last period. For all time of observations, the most rapid decrease in stickiness index took place for the following research groups:
1603 Demography --92%; 1301 Education Systems --83%; 0901 Aerospace Engineering --71%; 0307 Theoretical and Computational Chemistry --59%; 1101 Medical Biochemistry and Metabolomics --59%.
ANZSRC as any hierarchical classifying system tries to combine the similar objects in the same cluster and makes any two clusters dissimilar. Hence, a research group has to be more similar, has to have higher interaction with the research groups inside its division, than with the research groups from any other division. We checked all the research groups on base of their Jaccard index for 2016-2020 data and found 5 problem research groups according to proposed Assumption (Table 1
We analyzed the interaction of research divisions and research groups for 4 five-year periods. The level of interactions is assessed by Jaccard index. We analyzed paired and cumulative interaction for both research divisions and research groups. Only research groups of different research divisions were considered. Paired interaction allowed to find pairs that interact the most and analyze the behavior of different interactions over time.
Using paired interaction we analyzed leaders and the most changeable research divisions and groups in terms of interaction. Paired interaction for research divisions shows that every consecutive five-year period has decreased irregularity of its distribution of interaction. This also confirms the Gini index and the number of pairs with non-zero interaction. Cumulative interaction shows that all research divisions tend to have their stickiness decreased over time. The same effect shows Gini index for the stickiness index that decreases from 0.197 in the first period (2001)(2002)(2003)(2004)(2005) to 0.188 in the last period (2016-2020).
Paired interaction for research groups showed the same results but difference between two consecutive periods is greater by a larger factor. Cumulative interaction for research groups showed that with time research groups tend to have a more equally distributed stickiness index. It is also observed from the number of research groups that increased their stickiness index from zero to greater than zero and Gini index.
On base of interacting assessments during 2016-2020 we identified 5 research groups that have been assigned suspiciously to divisions in ANZSRC. They are as follows: 0105 Mathematical Physics, 0602 Ecology, 0909 Geomatic Engineering, 1502 Banking, Finance and Investment and 2001 Communication and Media Studies. All the mentioned research groups have at least a pair of more similar research groups in concurrent divisions with statistically significant level. Those 5 research groups also have strong semantic ties with concurrent divisions, this can be an argument for adapting of ANZSRC.