Introduction

Author co-citation analysis (ACA) is a bibliometric method in knowledge representation and has shown a good performance in depicting scientific intellectual structures and mapping knowledge domains (White and Griffith 1981; McCain 1990; Jeong et al. 2014). More than 3 decades since its born, ACA has been applied to many disciplines, such as library and information science (White and McCain 1998; Ding et al. 1999; Ding 2011a; Zhao and Strotmann 2014), cognitive science (Bruer 2010), management science (Eom 1999; Chen and Lien 2011; Zhao et al. 2017), and medical science (Chu et al. 2012).

Traditional ACA regards two authors with higher co-citation frequency as higher topical relatedness. Such assumption hints that every author pair with the same co-citation frequency as identical, which simply considers count- instead of content-based information. As the availability of full-text data nowadays, Jeong et al. (2014) firstly proposed content-based ACA method and compared the similarity between citing sentences. However, the computational cost of their content-based method could be high because of the processing of words as well as similarity calculation between citing sentences. Actually, with the full-text data we do not have to employ the content-level information; instead, several pieces of useful information at metadata level that were ignored previously in full text can be considered to improve the performance of ACA in mapping knowledge domains.

The number of mentioned times of references, for instance, is a typical piece of information. As pointed out by Ding et al. (2013) as well as Zhao et al. (2017), the number of mentioned times of a reference represents the importance of the reference to the citing paper. However, the traditional ACA regards as identical two co-cited authors with a distinct number of mentioned times in a citing paper, which is problematic. For example, Zhao and Strotmann (2014) cited (a) Zhao and Strotmann (2008a), (b) White and McCain (1998), and (c) Hirsch (2005), but (a) was mentioned 15 times, (b) twice, while (c) only once in the citing paper. The co-citation strength of pair (a)–(b) and (b)–(c) should be different when we consider their topical relatedness. In this paper, we start to consider the number of mentioned times of references as a supplement into ACA in order to provide more accurate information for mapping knowledge domains (Bu et al. 2017b).

Besides, the citing sentences containing references could have different numbers of words. From our intuitive thinking, a reference contained in a longer citing sentence should have more topical relatedness to the citing paper than that contained in a shorter one, because longer sentences are more likely to include more details or interpretations to the reference, which is more “useful” to the citing paper—otherwise it is not likely to be cited with many interpretative words. However, the traditional ACA ignores such difference in the length of citing sentences; as a result, we start to consider the difference in the length of citing sentence and combine it into ACA in this paper.

The current paper considers the number of mentioned times and the number of context words into ACA. The results of the empirical studies show that our newly proposed approach not only shows better clustering performance but also provides more details in knowledge domain mappings. As talked in the aforementioned paragraph, the current approach adopts full-text data without using content- or semantic information. This article is outlined as follows. At first, the work related to our study and the data with the methods for our analysis are detailed. The findings as well as the comparisons between the traditional ACA and our proposed method are then presented. Finally, the conclusions and the future research are pointed out.

Related studies

Author co-citation analysis (ACA) was proposed by White and Griffith (1981). In 1990, McCain gave a completed overview and set up a standard framework for ACA, in which four steps of ACA implementations were mentioned: (1) Data collection and processing; (2) Construction of raw co-citation matrix; (3) Transformation to correlation matrix; and (4) Data analyses (e.g., factor analysis, clustering analysis, multi-dimensional scaling (MDS) analysis, and network analysis) and result interpretations.

More than 30 years, this method has been improved a lot by revising rules to construct raw co-citation matrix [Step (2) above] and transform to correlation matrix [Step (3) above]. As pointed out by Persson (2001), the elements in co-citation matrix can be defined as first- or all-author co-citation frequency; the latter might, to some extent, provide more detailed knowledge domain maps (Eom 2008a; Rousseau and Zuccala 2004; Zhao 2006). As the availability of the all authors’ information, it is more common to use all authors’ information instead of first authors’ to run ACA. Meanwhile, the rules of defining main diagonal values was also discussed and at least six distinct ways of processing main diagonal values in raw co-citation matrix have been proposed and/or experimented (Eom 2008b). Additionally, several metadata of references, such as published time and venue of references and their keywords, were considered in ACA implementations (Bu et al. 2016), and they were found to play positive roles in improving the performance of ACA maps. Note that the metadata they employed had been obtained from reference lists instead of full text.

In the Step (3) above, we have also observed that many researchers have worked on the strategies of transforming correlation matrix (Ahlgren et al. 2003; White 2004). The usage of Pearson’s r and other correlation measurements has been debated in both theoretical and mathematical ways (Mêgnigbêto 2013). Although there is not any common-believed final conclusions about which measurement should be implemented in ACA, we here follow Ahlgren et al. (2003)’s arguments to use cosine similarity to transform the matrices in this work.

Due to the availability of full-text scientific data, Jeong et al. (2014) first explored content-based ACA by comparing the similarity between citing sentences. Their empirical studies show that content-based ACA is able to mine more details in scientific intellectual depicting compared with the traditional ACA. Nevertheless, the computational complexity is high in full text processing and semantic identification, which impedes the applications of their proposed method to various domains widely.

When full-text data are used, however, it is not required to make content- or semantic-level analyses. Several non-content-level metadata are easily accessible in full text, such as the number of mentioned times and the number of context words in a citing paper. In addition, these pieces of information reflect the importance of a certain reference to the citing paper. For example, if mentioned many times than others, a reference is likely to have more topical relatedness to the citing paper; if the citing sentence containing certain reference is longer than that containing another reference, we will be more confident to expect it to interpret more details and thus has higher possibilities to relate to the citing paper (Bu et al. 2017a). As a result, this paper combines the number of mentioned times and the number of context words of references into ACA and proposes a new method so as to improve the performance of ACA in knowledge domain mappings.

Methodology

The whole process of our algorithm is shown in Fig. 1. All of the dataset are derived from full-text in Journal of the American Society for Information Science and Technology (JASIST, currently named as Journal of the Association for Information Science and Technology). After data processing (see details in the “Data” section), we extract the number of mentioned times and the number of context words, and combine them into ACA (dotted area in Fig. 1, see details in the “Methods” section). After the new co-citation matrix is constructed, cosine similarity is utilized to transform it to correlation matrix. Factor analysis, network analysis, and MDS-measurement are used to analyze the data, in which Gephi (Bastian et al. 2009) is applied to display the results of the combined author co-citation network for discussions and analyses. Note that the dotted area in Fig. 1 is the major difference among the proposed and traditional ACA methods.

Fig. 1
figure 1

Flow diagram of the proposed algorithm

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Data

The dataset used in this research is the same as that in Jeong et al. (2014), in which 1420 full-text articles with citation links published in JASIST between January 2003 and June 2012 are selected. These 1420 articles containing 60,068 references are completed by 32,095 authors. In order to make the co-citation matrix denser, we extract the most popular 500 authors who have received the most number of citations; bibliometrically, the most “popular” scholars are often regarded as the representative of the research going back according to Zhao and Strotmann (2008a, 2014).

Methods

Calculation of mentioned time parameters

A paper citing other papers refers that these cited papers (references) are related and useful to the citing paper (CP). Traditionally, these co-cited papers are regarded as equal in co-citation analysis (Ding et al. 2013). However, the importance of cited papers might be distinct (Cano 1989; Case and Higgins 2000). Specifically, some references are crucial to the CP because they might be the foundation of CP. In the full-text, the important references can be revealed as multi-mentioned cited papers. For one CP, from an intuitive thinking, the more number of mentioned times a certain reference has, the more importance it is to the CP (Ding et al. 2013; Zhao et al. 2017a, b; Zhu et al. 2015). For instance, Zhao and Strotmann (2014) cited (a) Zhao and Strotmann (2008a), (b) White and McCain (1998), and (c) Hirsch (2005), but (a) was mentioned 15 times, (b) twice, while (c) only once. In this case, (a) should be the most correlative reference to the CP, compared with (b) and (c). Indeed, Zhao and Strotmann (2014) tried to map the knowledge domains of information science (IS) between 2006 and 2010 while (a) did the same thing but between 1996 and 2005 with similar methods, ACA and author bibliographic coupling analysis (ABCA), which shows that (a) is closely-related to the CP. However, (b) only used ACA to map the knowledge domain of IS instead of ABCA and the result of (b) is also very different from (a) and the CP. The reason (c) is cited is simply because the indicator “h-index” was used and mentioned. Hence, we can see that the number of mentioned times of a reference is indeed positively related to its relatedness with CP.

Similarly, in ACA, if two co-cited authors are both mentioned many times in a CP, their topical relatedness tends to be high because both of them are closely related to the CP. In the above example, the topical relatedness of (a)–(b) should be higher than that of (b)–(c). Indeed, (a) and (b) both focused on mapping the field of IS by employing ACA, but (c) simply introduced an indicator to evaluate scholars. Thus, in our proposed algorithm, we assume that two co-cited authors with more number of mentioned times should be assigned more weights in co-citation analysis because they have higher possibilities to be related with each other topically.

Mathematically, suppose that the authors Ai and Aj are co-cited for xij times. Specifically, the CP is annotated as \(P_{ij\_1}\), Pij_2, …, \(P_{{ij\_x_{ij} }}\). In Pij_k (\(k = 1,2, \ldots , x_{ij}\)), assume that the author Ai is mentioned for λik times and the author Aj is mentioned for λjk times. If we annotate the mentioned time of the cited author with the maximum number of mentions in the paper Pij_k as λk_max, the mentioned time parameter between the authors Ai and Aj in the paper \(P_{ij\_k}\), MTij_k, is calculated as:

$${\text{MT}}_{ij\_k} = \frac{{\lambda_{ik} \lambda_{jk} }}{{\lambda_{{k\_{ \hbox{max} }}}^{2} }}$$
(1)

If we consider all of the MTij_k in citing papers \(P_{ij\_1}\), Pij_2, …, and \(P_{{ij\_x_{ij} }}\), the mentioned time parameter between the authors Ai and Aj among dataset, MTij, could be defined as:

$${\text{MT}}_{ij} = \mathop \sum \limits_{k = 1}^{{x_{ij} }} {\text{MT}}_{ij\_k}$$
(2)

Calculation of context word parameters

When citing references, CPs tend to use one or more sentences to set up an argument, which is called citing sentences (or “citance” proposed by Nakov et al. 2004) (Jeong et al. 2014). However, the lengths of citing sentences are probably different. For example, Zhao and Strotmann (2014) cited: (a) Finlay et al. (2012), (b) Milojević et al. (2011), as well as (c) Sugimoto et al. (2011) in the same sentence with 27 words. They shared these 27 words and each of them has been assigned nine words averagely. Meanwhile, Zhao and Strotmann (2014) also cited (d) Zhao and Strotmann (2008b) in a sentence with 31 words. Although all of these references are cited once in the CP, their numbers of context words assigned are diverse, 9, 9, 9, and 31, respectively.

Basically the number of context words assigned in a CP reflects the importance of the reference. Specifically, more numbers of context words assigned in a CP reveal that more details and interpretations of the reference is likely to be stated, which hints that it has higher topical relatedness to the CP. For example, CP uses ACA and ABCA to map the knowledge domain of IS field, while (d) explores AACA at a methodology level; both of them are closely related to the ACA research. Nevertheless, (a) analyzed Library Science (LS) using titles and keywords, (b) employed article title words to depict the scientific structure of LIS, and (c) focused on North American LIS dissertation using Latent Dirichlet Allocation (LDA) model, all of which are not as close as (d) in terms of the topical relatedness with the CP from an intuitive perspective. Indeed, the number of context words assigned to (d) is much more than that to (a), (b), and (c). These show that the number of context words assigned in a CP is positively related to its topical relatedness to the CP. Similarly in ACA, if two co-cited authors are both assigned many words than others, their topical relatedness should be higher because both of them are closely related to CP.

To test this assumptions, we randomly select 150 citing sentences from all citing sentences in our corpus. Then two bibliometricians manually labeled the importance of the references containing in the sentences to the raw papers; specifically, they labeled the importance as “important”, “neutral”, and “unimportant”. In total, their labels on 138 sentences out of 150 (92%) are consistent; we therefore target on these 138 citing sentences. We then implement a mean-based t test and found a significant difference in regard to the length of the citing sentences (i.e., the number of context words in the sentences) among the three groups.

In Pij_k, assume that during its μth mention (μ = 1, 2, …, λik), the citing sentence containing the author Ai (Aj) includes wikμ (wjkμ) words and mentions aikμ (ajkμ) distinct authors (\(w_{ik\mu } ,w_{jk\mu } , a_{ik\mu } , , a_{jk\mu } > 0\)). The number of context words of the author Ai in the paper Pij_k, cwi_k, can be calculated as (similar to Aj):

$${\text{cw}}_{i\_k} = \mathop \sum \limits_{\mu = 1}^{{\lambda_{ik} }} \frac{{w_{ik\mu } }}{{a_{ik\mu } }}$$
(3)

If we annotate the largest number of context words of cited author in the paper Pij_k as cwk_max, the context word parameter between the authors Ai and Aj in the paper \(P_{ij\_k}\), CWij_k, is calculated as:

$${\text{CW}}_{ij\_k} = \frac{{{\text{cw}}_{i\_k} {\text{cw}}_{j\_k} }}{{{\text{cw}}_{{k\_{ \hbox{max} }}}^{2} }}$$
(4)

If we consider all of the CWij_k in citing papers \(P_{ij\_1}\), Pij_2, …, and \(P_{{ij\_x_{ij} }}\), the context word parameter between the authors Ai and Aj among dataset, CWij, could be defined as:

$${\text{CW}}_{ij} = \frac{1}{{x_{ij} }}\mathop \sum \limits_{k = 1}^{{x_{ij} }} {\text{CW}}_{ij\_k}$$
(5)

Construction of the co-citation matrix based on the two parameters

The co-citation matrix in our proposed algorithm is based on the above parameters to be normalized into [0, 1]. We here annotate the largest co-citation frequency among the dataset regardless of which author pairs as xmax, and the weight values for co-citation, mentioned time, and context word parameters as wc, wMT, and wCW, respectively. To better compare different parameters, we run four different models based on these parameters. In Model 0, we simply employ the traditional ACA without importing any other factors. The co-citation matrix in Model 0, M0 = (m1,i,j), as:

$$m_{0,i,j} = \frac{{x_{ij} }}{{x_{ \hbox{max} } }}$$
(6)

In Model 1, we combine the raw co-citation matrix with the mentioned time parameter; we construct the new co-citation matrix in Model 1, M1 = (m1,i,j), as:

$$m_{1,i,j} = w_{\text{c}} \cdot \frac{{x_{ij} }}{{x_{ \hbox{max} } }} + w_{\text{MT}} \cdot {\text{MT}}_{ij}$$
(7)

where wc + wMT = 1.0. In Model 2, we combine the raw co-citation matrix with the context word parameter; thus the new matrix in Model 2, M2 = (m2,i,j), as:

$$m_{2,i,j} = w_{\text{c}} \cdot \frac{{x_{ij} }}{{x_{ \hbox{max} } }} + w_{\text{CW}} \cdot {\text{CW}}_{ij}$$
(8)

where wc + wCW = 1.0. In Model 3, we combine the raw co-citation matrix with both of the two parameters; thus the new matrix in Model 3, M3 = (m3,i,j), as:

$$m_{3,i,j} = w_{\text{c}} \cdot \frac{{x_{ij} }}{{x_{\hbox{max} } }} + w_{\text{MT}} \cdot {\text{MT}}_{ij} + w_{\text{CW}} \cdot {\text{CW}}_{ij}$$
(9)

where wc + wMT + wCW = 1.0. Essentially the Model 0 acts as a baseline for comparing with other models.

Results and discussion

Factor analysis

In factor analysis, we extract the factors whose Eigen factor is 1.0 or more as the result of factor analysis, regardless in Models 0–3. We have known that the model becomes more complex and involves more information from Model 0 to Model 3. As shown in Table 1, the number of factors extracted from Model 3 is 16, which is five more than that in the traditional ACA (i.e., Model 0). Models 1 and 2 are found to extract 13 factors in the experiments. In terms of the total variance explained, the factor analysis of Model 0 is able to explain about 82.8% of total variance while that of Model 3 explains 85.6%.

Table 1 Factor analysis results overview
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Based on some previous research (Janssens et al. 2006; Yang et al. 2016), several core sub-fields of information science are dug out and more details are supposed to be refined. Table 2 shows the factor analysis results of all four models. Core sub-fields of Library and Information Science are extracted and identified by all methods (models), including: (1) information retrieval, (2) information seeking behavior, (3) language model, query, and clustering, (4) text mining, machine learning, (5) user interface, (6) evaluation indicator, index, (7) webometrics, social network analysis, (8) scholarly communication, (9) journal citation analysis, interdisciplinarity, evaluation of algorithms, (10) network analysis, and (11) bioinformatics. Although bioinformatics is not the main scope of JASIST, there is still one author, Don Swanson, appearing in that factor, which confirms Jeong et al. (2014)’s result.

Table 2 Factor analysis results
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Although using the same dataset as Jeong et al. (2014), we input approximately 500 authors into factor analysis while Jeong et al. (2014) did 100. We try to compare our results with theirs, which shows in bold in Table 2, where we can find that the results are similar and confirm each other’s. The factors extracted by Models 1 and 2 are more in detail than Model 0, i.e., the baseline. On the other hand, with respect to the factor analysis result of Model 3, we can find many detailed sub-fields of information science, such as visualization and data mining. These newly-detected domains are able to showcase the nuance and the emerging topics of information science recently. Therefore, we believe that our proposed methods, when inputting more metadata in full text into ACA, can reveal more details and nuance in depicting scientific intellectual structures.

Network analysis

Figures 2, 3, 4 and 5 show the scientific intellectual structures by using the four models, respectively, where each node represents an author and the size of the node is proportional to the degree of the node in the given network. The distance between nodes are determined by ForceAtlas2 (Jacomy et al. 2014), a frequently used layout algorithm in Gephi. If two nodes lie near in the map, for instance, their relationship could be strong; and vice versa. For visualization, we employ Modularity algorithm (Blondel et al. 2008), in which nodes classified in the same cluster have significantly more links than those in different clusters, compared with a null model. Based on the results of Modularity algorithm, we assign nodes with different colors. The nodes (authors) within the same color indicate that their research interests are similar, while those in different colors show that their research interests should be distinct. The labels of the clusters are manually given by our reading literatures of the authors as well as browsing their personal websites. From Fig. 2 we can see that four clusters are detected, bibliometrics, information retrieval, information behavior, and library science/qualitative research. The results are similar to Jeong et al. (2014)’s result, where they also found four clusters, bibliometrics, information retrieval (I), information retrieval (II), and library science. Moreover, Figs. 3 and 4 detect five clusters; besides four clusters having been detected in Fig. 2, it also finds “test mining/data mining”. In Fig. 5, another cluster, namely “network-based information science” is detected. These two new clusters reveal the nuance of the development of IS and are micro-level sub-fields in IS. These indicate that our proposed models provide more details in knowledge domain maps and help better understand the domain, and that the more full text-based metadata involved, the more details we can obtain.

Fig. 2
figure 2

Knowledge domain map: Model 0 (traditional ACA)

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Fig. 3
figure 3

Knowledge domain map: Model 1

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Fig. 4
figure 4

Knowledge domain map: Model 2

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Fig. 5
figure 5

Knowledge domain map: Model 3

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Intuitively, the nodes within the same cluster lie nearer, and the nodes in different clusters lie farther in Figs. 3, 4 and 5 than in Fig. 2; and those distances are larger in Fig. 5 than in Figs. 3 and 4. These indicate a better clustering performance in Models 1–3 than Model 0 and better in Model 3 than Models 1–2. Take K. W. McCain and R. Rousseau as examples. Both of them focus on bibliometrics during their main scientific careers. Specifically, they are both interested in ACA, where McCain (1990) gave a comprehensive overview of ACA and used ACA to map knowledge domain of IS field between 1972 and 1995 (White and McCain 1998). Rousseau proposed several types of ACA by classifying them according to distinct requirements (Rousseau and Zuccala 2004) and discussed whether Pearson’s r should be used in ACA (Ahlgren et al. 2004). Their positions in Figs. 3, 4 and 5 are nearer than those in Fig. 2, which shows that the proposed method plays a role of closing authors with similar research interests. Another examples come from A. Spink and B. Shneiderman, in which the former researcher is an expert in information seeking behavior (Spink et al. 2002; Spink and Cole 2005) while the latter has been concentrating on user behavior analysis (Shneiderman 1978). We know that both of them are behavior scientists. Although the nodes representing these two authors are not closely with each other in Fig. 2, they move nearer in the visualization of new proposed models. However, the distance between Spink and McCain becomes farther in Figs. 3, 4 and 5 than Fig. 2, indicating that our proposed method separates authors sharing different research interests in knowledge domain maps. All of these facilitate the quality of maps in terms of the clustering performance.

To understand the difference among methods more clearly, we compare two properties of the networks generated by our four methods, network density and average clustering coefficient (ACC). We know that all networks are weighted instead of binary, i.e., the edges in the networks range from zero to a certain positive number but not purely zero and one; therefore, to calculate the properties, we employ Barrat et al. (2004)’s algorithm. Based on network science theories, a denser network indicate more interactions among nodes—in the case of scientific intellectual structures, more pieces of information are therefore presented; a network with greater ACC shows a better clustering performance. Table 3 shows the density and ACC for networks generated by four methods, in which we can find that Model 0 (traditional ACA) has a low density, but when we add the factor of mentioned time or context word, the density of the network increases. If both factors are involved, the density doubles compared with that in Model 0. In terms of the ACC, we find that when more metadata in full text are employed, the values of ACC raise. All of these descriptive statistics indicate that our proposed ACA methods combining metadata in full text enhance the clustering performance and provide more information in scientific intellectual structure depicting, which echoes our findings in the aforementioned sections.

Table 3 Descriptive statistics of the network properties in all implemented methods
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MDS-measurement

In order to evaluate the performance of our proposed method quantitatively, we employ multi-dimensional scaling measurement (MDS-measurement) (Bu et al. 2016) to supplement our qualitative arguments in the “Network analysis” section. Different from MDS that is a typical way to show nodes in a two- or three-dimensional map (essentially a visualization algorithm), MDS-measurement, a bibliometric indicator to evaluate the clustering performance provided by MDS, aims to calculate the MDS-measurement value (σ), which is equal to the ratio between the sum of the distance between the nodes within the same cluster (c), and the sum of the distance between the nodes in different clusters (S), i.e., σ = c/S. Intuitively, a smaller σ indicates better clustering performance in knowledge domain maps in which nodes within the same cluster lie nearer while those in different clusters lie farther. Table 4 shows the MDS-measurement result, where we can see that the MDS-measurement value (σ) of Models 1–3 is smaller than that of Model 0 (traditional ACA), indicating a better clustering result in knowledge domain map. Also, σ in Model 3 is the smallest among Models 1–3, showing that the cluster performance of Model 3 is the best among our proposed methods. This confirms our observation in the “Network analysis” section.

Table 4 MDS-measurement results
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Conclusion

This paper proposes a novel method combining the numbers of mentioned times and context words into traditional author co-citation analysis (ACA). The results show that compared with the traditional method, our newly proposed approach not only shows better clustering performance but also provides more details in knowledge domain mappings. Considering that this method does not need a large volume of calculation such as content-based ACA (Jeong et al. 2014; Kim et al. 2016; Hsiao and Chen 2017), we believe that our proposed method are easily applied to various disciplines so as to depict scientific intellectual structures by involving more information and improving the traditional ACA.

Besides the method itself and its advantages compared with the traditional ACA, this study provides several implications to the future researchers. Firstly, we use full-text data but not intend to analyze content- or semantic-level information, which breaks the conventional thinking to use complex natural language processing technologies aiming at mining content- or semantic-level data so as to map knowledge domains. Secondly, our approach inspires future researchers to duplicate this method on other scholarly network analyses, such as author bibliographic coupling analysis (Zhao and Strotmann 2008a) and coauthorship analysis (Bu et al. 2017a; Ding 2011b; Zhang et al. 2018). Specifically, the metadata in full text can be involved into an author bibliographic coupling network by normalizing and assigning certain weight values. Furthermore, this research supplements the framework of bibliometric elements proposed by Morris and Vander Veer Martens (2008), in which papers, paper authors, paper journals, references, reference authors, reference journals, and index terms are included. Our study provides “citing sentences” as a bridge between “papers” and “references”, and shows the potential detailed affiliations upon “citing sentences” such as the number of mentioned times and the number of context words of references. These have offered significant foundations for future supplements of the bibliometric element framework when more full-text data are involved.

Nevertheless, simply duplicating this method is not always wise. Although we find that our method can mine more details that traditional ACA cannot do, a combination between traditional method and our proposed approaches should often get much better performance. Combining two methods can provide more distinct perspectives to make sense on the bibliometrical relationship among authors from a retrospective view. Practically, if many full text-based metadata have been extracted from the raw dataset, a traditional ACA will also be doable.

One of the key steps of our proposed method is aggregating paper- into author-level information. For instance, when calculating the mentioned time parameter, we first do the parameter in a given paper and then aggregate it to a given author by calculating the mean values. Following this idea, we can then aggregate the parameters into other levels, including topics, journals, and even disciplines.

However, there are several limitations in this research. For example, we only used first authors’ information instead of all authors’. The accuracy might thus be negatively affected. Moreover, there are still many other types of metadata that are not used to involve in ACA in previous or the current studies, such as the sequence of co-cited authors (He et al. 2012) and the number of figures or tables (Lee et al. 2018). We would like to focus on these under the context of ACA as well as other scholarly network analyses in the future.