Related work

Mapping the structure and evolution of scientific fields has been an active area of research. Prescribed taxonomies and discipline classifications have been widely used to categorise papers into broader subjects or research areas [8–10]. For example, Microsoft Academic and Web of Science maintain large, subject or ‘field-of-study’ classifications for articles that are readily available and provided at multiple levels of detail. However, such top-down, static, taxonomies struggle to accurately capture the organic evolution of research topics [11–13], as disciplinary borders have been shown to be changing constantly [14]. Alternative, bottom-up methods have been developed to identify the constituent research topics in some larger corpus. In particular, keyword-based methods identify research topics as groups of commonly co-occurring keywords [15–18], while topic modelling techniques can be applied to research papers’ titles, abstracts, or full texts to group or connect papers that exhibit similar patterns of word usage [19, 20]. Such bottom-up methods have advantages over static, prescribed classifications as they can be adapted to the specific application/dataset. Some works have developed these methods to study the evolution of topics and keywords over time [10, 17, 21, 22]. However, topic modelling methods come with challenges related to model selection and validation [20]. Moreover, they fail to recognise the transfer of knowledge inherent in a corpus of scientific research, in particular: the knowledge transfer represented by citations relationships.

Network analysis approaches have emerged as powerful tools for mapping the landscape of scientific research directly from citation patterns [23–27]. Community detection algorithms aim to identify densely connected groups of nodes in networks, representing communities or clusters with strong internal connections and relatively fewer external connections [28]. These algorithms have found numerous applications in various domains, including social network analysis [18, 29, 30], biological networks [31], and network science [28]. By modelling scientific literature as networks of papers connected by citations, community detection methods can uncover the underlying research areas present as groups of related papers that share knowledge sources and/or knowledge outputs. As research fields evolve over time, the underlying network structures and community memberships change, necessitating the study of dynamic communities. Dynamic community detection algorithms have been developed to track the evolution of communities in social networks [4, 32]. Building on works in dynamic or ‘evolutionary’ clustering [33, 34], many dynamic community finding techniques partition the data into a series of temporal snapshots or time windows [4]. By matching communities identified in adjacent networks snapshots, dynamic community life-cycles are identified as sequences of matched snapshot communities [26, 32, 35]. Existing literature has proposed various metrics specific to dynamic communities, such as ‘stability’ [36], ‘stationarity’ [32], and ‘density’ [36], and developed methods for identifying and characterising life-cycle ‘events’, such as community births, deaths, merges, and splits.

Several studies have applied dynamic community analysis techniques to citation networks. Many of the earliest examples include dynamic citation networks as case-studies, where the specific focus of the work is to demonstrate the performance of their proposed community finding methods [14, 37]. Subsequent works have had a more explicit focus on mapping or predicting changes in research networks. For example, Chakraborty et al. [8] measure changes in various citation network metrics for different fields-of-study, as prescribed by the Microsoft Academic Graph. Similar works track changes in community metrics for fields identified in a bottom-up manner using community detection [26, 38], while others focus on predicting future changes [25]. Further examples of dynamic community finding in research networks build multi-partite graphs of papers, authors, concepts and/or venues, in order to uncover the social dynamics that define the formation of research areas [24, 39]. To date, there has been limited research that leverages dynamic community finding in citation networks to study knowledge transfer between disciplines.

Effective knowledge transfer and integration across different disciplines are crucial for addressing complex scientific challenges and driving innovation [1, 2]. However, interdisciplinary research often faces significant hurdles, such as insular reading and citation practices [40]. Such barriers can lead to the formation of knowledge gaps and silos, hindering scientific progress and productivity [41, 42]. Identifying and bridging these knowledge gaps is essential for fostering interdisciplinary collaboration and facilitating the cross-pollination of ideas and methods. For example, [43] identify research gaps as keyword pairs that co-occur significantly less often than predicted. Papers that span these gaps (i.e., contain both keywords) were found to have a high impact. Several studies have recognised the presence of knowledge silos and their detrimental effects on scientific research, emphasising the need for approaches to map and understand knowledge transfer dynamics [40–42]. However, limited research exists to date that studies knowledge transfer from the perspective of dynamic citation network analysis. Instead, works in this area typically rely on prescribed field of study or discipline labels [43, 44].

Karunan et al. [45] studied cross fertilisation between research areas through the study of ‘boundary papers’ – i.e., papers that are identified in more than one field. The authors defined fields at the time of data collection via a set of custom keywords chosen to relate to each research area. Similarly, Zhou et al., [44] identified research disciplines according to the journal in which they were published and characterised the knowledge flows between disciplines in terms of their ‘broadness’, ‘intensity’, and ‘homogeneity’.

In this work, we extend existing methods for finding dynamic communities to specifically map knowledge transfer and identify knowledge gaps in citation networks. Crucially, citation networks have unique characteristics, such as cumulative growth, where papers and citations are never removed from the network, and content-rich nodes, where papers include substantial textual information. These features necessitate novel approaches to community detection and tailored strategies for interpreting their outputs. The primary goal of many existing applications of dynamic community finding in citation networks is to benchmark the performance of proposed algorithms [37, 46], rather than to understand the real-world dynamics of interdisciplinary or multidisciplinary research interactions. Therefore, they often overlook the specific properties and nuances of cumulative citation networks and fail to explain how to interpret the resulting dynamic communities. Furthermore, while the textual metadata associated with papers has been highlighted as an important resource for citation network analysis [5], many instances of such analysis have been found to ignore the article content [6]. Leveraging this textual information can help validate and interpret the identified communities. Specifically, dynamic community metrics which consider the content of the papers in addition to community membership and network structure, could serve to bridge the gap between network-based methods of tracking research evolution and other NLP-based approaches (e.g. [10, 17, 21]).

Step communities

To investigate the life-cycles of research areas within a specific body of work, we require a citation network that evolves over time. In this work, we adopt a discrete time dynamic network such that the citation network is described by a sequence of time step graphs , where each time step graph is defined by a set of nodes and edges . Each set of nodes contains the papers present in the network at time step t and the set of edges E_t represent the citations between them. Due to the cumulative nature of citation networks, discrete time dynamic citation networks represent a unique type of dynamic network. Specifically, nodes (papers) and connections (citations) are never removed from the network. As such, the set of time step graphs are cumulative, i.e. . In this application, we divide the citation network by year, such that the step graph denoted by G₂₀₁₀ contains all papers in the dataset published before 2011.

Labelling step communities.

Following [25, 38], we use the title and abstract text of the papers in a community to annotate the community’s topic. Specifically, we combine the terms from all the papers in a community into a bag-of-words vector. We then annotate each community using the top-n terms according to the Term Frequency inverse Community Frequency (TF-ICF). The ICF terms used to adjust the term frequencies are calculated per year. In addition we consider the category term descriptor (CTD) [52]. We treat each community as a category and calculate CTD based on:

(1)

Here C denotes the set of communities, CF(t_k) is the community frequency of term t_k, and is the document frequency for term t_k in community C_i.

Measuring knowledge transfer.

In addition to characterising individual communities, at each time step we construct a community interaction network to model knowledge transfer between the identified research areas. In the interaction network at time step t, the set of nodes corresponds to the step communities discovered at time t and the set of edges correspond to the citations between them. Formally, I_t has the set of nodes , and the set of weighted edges J_t such that . Here is the probability of an interaction/citation between papers in and , given in Eq 2.

(2)

While the strength of the connections in the community interaction network reveal the extent of the knowledge transfer between two research areas, we can also consider standard network measures to summarise the nature of knowledge transfer for any given research area. Specifically, we rely on two primary perspectives to summarise knowledge transfer for a research area.

First, network proximity measures help us to understand citation behaviours between two specified topics or communities. The connection strength between two communities in the interaction network is considered as the ‘first-order’ network proximity. According to the above definition of the interaction network, the connection strength or edge weight between two communities is the probability of a citation between a paper in each community. For example, if 10% of the articles in research area A cite 10% of the articles in research area B, then the pair of communities will have a first-order proximity or ‘interaction probability’ of 0.01 or 1%. In typical, real-world citation networks, which contain large communities or research areas, community interaction scores above 1% would indicate a moderate-high level of knowledge transfer. However, as the probabilities are normalised with respect to the size of the communities, we recommend studying the interactions comparatively. See Figs 6 and 7 for examples. The ‘second-order’ network proximity of two communities is a measure of the similarity of the neighbourhoods of the communities. Thus, two communities will have high second-order proximity if they have similar citation behaviours with the other topics in the network. We measure second-order proximity as the cosine similarity between the community’s interaction probabilities across the network, that is, between their respective columns of the weighted adjacency matrix describing the community interaction network.

Second, network centrality measures reveal the extent to which topics are involved in the transfer of knowledge in the network. The unweighted degree centrality of a community in the interaction network reports the number of communities with which that topic shares knowledge, while the betweenness centrality measures the importance of that node in facilitating knowledge transfer across the network.

Dynamic communities

The previous sections detailed how we identify step communities in individual time step graphs. A key goal is to track the evolution of these communities over time. This section outlines our approach for constructing dynamic community life-cycles by linking step communities across time steps. This allows us to analyse how research areas emerge, grow, merge, split or dissipate as the field evolves.

Finding and tracking dynamic communities.

We follow the method proposed in [35] to track the life-cycles of communities in a cumulative citation network. In this framework, the step communities in the time step graphs represent observations of dynamic communities at a given time point (year). If we denote the set of step communities identified by OSLOM at time t as , a dynamic community can be then represented by a chronology of step communities, for example . At the first time point t₀, dynamic communities are formed using a one-to-one with the step communities . Subsequent step communities are added to the dynamic communities using a heuristic, many-to-many mapping. The most recent step community in a dynamic community is called its ‘front’. At a given time step, comparing the step communities with all of the dynamic community fronts can lead to a number of possible events:

1. If a step community does not match with any of the dynamic community fronts, it is added as a new dynamic community with a single step. This is known as community birth.
2. If a step community matches with a single front, that step community is added to that dynamic community timeline and becomes the new front.
3. If two or more step communities match with the same front, then new identical dynamic communities are formed and one of the matching step communities is added to each to act as it’s front. This is known as community splitting.
4. If a step community matches with multiple fronts, then it is added to each of them. This is known as community merging.
5. If a dynamic community front does not match with any of the step communities then the front is not updated. The front may match with step communities at subsequent time steps, thus allowing for intermittent community structures to be found. If the front does not match with any of the step communities in any of the subsequent time steps then this is known as community death.

To match community fronts with step communities, we follow the strategy proposed by [35]. Given a step community and dynamic community front F_j, we compute the similarity between , F_j as:

Using the above measure for similarity, we match step communities to front if the similarity exceeds a matching threshold .

Characterising dynamic communities.

To analyse the properties and evolution of dynamic communities tracked across time steps, we propose a set of six metrics. The first metric is the community lifespan, measured as the number of time steps in which it is present in the dynamic network. We then consider four metrics derived from time series data of the community’s constituent step communities at each time point. The community size time series tracks the number of papers belonging to the step communities over time. The degree centrality and betweenness centrality time series measure how central the step communities are within the community interaction network in facilitating knowledge flow. The final two metrics aim to quantify the stability and coherence of a dynamic community’s research focus as it evolves, similar to existing approaches taken in NLP-based studies of research topic evolution [10, 17]. The content coherence metric compares the textual similarity of papers between consecutive step communities. Specifically, for a dynamic community , we compute the average pairwise cosine similarity between the SciBERT topic embeddings of papers in and at each time step t. This yields a time series capturing how coherent the research topic remains. Similarly, the membership stability metric tracks changes in the specific paper membership of the community over time. It is calculated as the Jaccard similarity between the paper sets of consecutive step communities and in the dynamic community D.

While metrics like size and centrality characterise the community’s position and importance in the network, the content coherence and membership stability allow analysing the thematic evolution of the underlying research area. In most cases, we summarise the time series values using averages over the community’s lifespan or specific time periods of interest.

Research questions

Given the above described framework for discovering, interpreting and characterising research areas in some corpus, in this section we outline how our proposed methods can be used to answer our three key research questions from the Introduction relating to knowledge transfer in XAI research.

1. To what extent do contemporary topics in the literature rely on foundational research in psychology, statistics and computer science? We answer this question in a number of steps:
   1. (a) Identify the foundational topics in the literature as long-lived communities with coherent subject matter that are consistently central in the interaction networks.
   2. (b) Identify contemporary topics as the communities present in the later periods of the dataset that are populated by the most recent papers.
   3. (c) Separate and compare those recent communities that cite the foundational topics from those that do not.
2. What are the research areas that are most isolated in terms of knowledge transfer within the literature? We refer to these isolated research areas as ‘knowledge silos’, and we identify them as the nodes with the lowest total interaction probability in the community interaction network.
3. Is there evidence of knowledge gaps between otherwise related research areas?/What are the most significant knowledge gaps in the literature? Our approach to identifying knowledge gaps is outlined below:
   1. (a) Use a regression model to predict interaction probabilities in the community interaction network based on the research areas’ content similarity and citation neighbourhood proximity. Specifically, we use a regression model with a gamma distribution (implemented in Python 3.9.7 using Scikit-learn [55]) to predict the interaction probabilities between all pairs of communities in the final time step graph. The independent variables are: 1) the average pairwise cosine similarity between the SciBERT embeddings of papers in each community (content similarity), and 2) the cosine similarity between the communities’ connection probabilities in the interaction network (second-order network proximity capturing similarity of citation neighbourhoods). SciBERT embeddings are learned from the papers’ title and text using a pre-trained transformer language model (SciBERT [56]) provided by HuggingFace.
   2. (b) Analyse the residuals: Pairs of communities with large positive residuals from the model predictions are then identified as having knowledge gaps, since they demonstrate far less knowledge transfer than expected given their content relatedness and structural proximity in the network.
   3. (c) Highlight research areas that exhibit multiple large positive residuals and examine these knowledge gaps.

Preliminary results—community life-cycles

In this analysis, since we investigate knowledge transfer in the area of XAI-related research, we consider communities discovered at the lowest level of the OSLOM hierarchy. To demonstrate our approach and to provide context for our definition and discovery of research areas, we provide two examples of community life-cycles in the flow diagrams in Figs 2 and 3. In total, we identify life-cycles for 435 dynamic communities or research areas. Of these areas, 163 dissolve before the final time step in 2023. Research area sizes range from 3 to 320 papers, with a median size of 50. We choose the two examples in Figs 2 and 3, as they represent long-lived communities with different characteristics. Moreover, both of these example research areas are relevant to discussion in the following sections, as they are identified as foundation topics in the XAI literature. The flow diagram presented in Fig 2 shows the life-cycle of a research area. In particular, the figures shows how the research area relating to regression models ‘dissolves’, as its constituent papers are cited by work in many other topics. Dynamic community ‘death’—as it is described in the social network analysis literature—has some specific caveats in the context of citation network analysis. Specifically, as nodes and connections are not removed from the network, community ‘death’ only occurs in the form presented in Fig 2, where a community dissolves as the strength of connections between community’s members are surpassed by connections to external works. Crucially, we note that the community dissolution shown here is specific to the perspective of our dataset (i.e., of XAI-related research), as the works in the community pick up citations from the many other research areas where XAI methods can be applied or extended. In an analysis with a different focus – given another subset of the surrounding research – it might be seen that the regression community remains intact, or instead that the regression topic is realised by multiple, more specialised research areas. This flexibility is one of the benefits of bottom-up data driven classifications for research articles. Such classifications should be specific to the analysis, as there is no unique map of science [11].

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Fig 2. Life-cycle of regression models research.

Flow diagram showing the life-cycle of a dynamic community pertaining to statistics research on regression models. Any papers present in the first or last realisation of the dynamic community are plotted. The nodes in the graph represent step communities and they are grouped by the time step in which they appear. The edges between nodes show the movement of papers between step communities. The dynamic community dissolves after 2010

https://doi.org/10.1371/journal.pone.0329302.g002

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Fig 3. Life-cycle of neural networks research.

Flow diagram showing the life-cycle of a dynamic community of neural networks research that splits before 2005. The research area that focuses on rule extraction remains present in 2020. Any papers present in the first or last realisation of the dynamic community are plotted. The nodes in the graph represent step communities and they are grouped by the time step in which they appear. The edges between nodes show the movement of papers between step communities.

https://doi.org/10.1371/journal.pone.0329302.g003

For comparison, we include the life-cycle of another, more stable, research area in Fig 3. In this example, we can see that the community of neural network research splits some time before 2005 into works on ‘rule extraction’ and ‘recurrent’/ ‘connectionist architectures’. The ‘rule extraction’ community continues to grow steadily after this point, while the remaining connectionist computing community dissolves into various applications and sub-fields related to Deep Learning and its applications in XAI.

As a final preliminary result, in Fig 4 we compare the life cycles of research areas related to two important methods in the domain of XAI: ‘causal explanations’ and ‘counterfactual explanations’. It is apparent from the flow diagram that these two research areas have evolved in very different ways. Specifically, the causal explanations community appears at the confluence of multiple research areas that are spread across different fields of study (Computer Science, Statistics, and Psychology) and consisting of research published prior to 2010. By comparison, the counterfactual explanations community emerges rapidly and includes very little research predating 2020. As research outputs are grouped into research areas based on shared knowledge sources, the life cycles as presented indicate that the causal explanations research relies more on established literature from the fields of Psychology, Statistics and Computer Science, in contrast to the community of counterfactual explanations research. In the following section, we further assess the extent to which contemporary research areas in XAI rely on foundational knowledge, by directly measuring the knowledge transfer between research areas.

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Fig 4. Life-cycles of counterfactual and causal explanation methods.

Flow diagram comparing the life-cycle of two dynamic communities relating to two general approaches to explanation: ‘causal explanation’ and ‘counterfactual explanation’. Any papers present in the final realisation of either dynamic community are plotted. The nodes in the graph represent step communities and they are grouped by the time step in which they appear. The edges between nodes show the movement of papers between step communities.

https://doi.org/10.1371/journal.pone.0329302.g004

Knowledge transfer from foundational research areas

We now assess the extent to which contemporary research areas in the field of XAI rely on the theoretical and methodological foundations of the literature. This analysis consists of three steps. In the first two, we identify foundational and contemporary research areas based on the dynamic community characteristics proposed in the Methods and Materials section, before using community interaction probabilities to measures the knowledge transfer between areas.

Firstly, we identify foundational areas in the literature as long-lived dynamic communities, which are important to the knowledge transfer in the field in the earlier portions of the dataset. Fig 5 shows a simplified view of the life-cycles of the dynamic communities with the highest (left) and lowest (right) betweenness centrality scores, as measured in the community interaction network in the period 2000–2010. We rely on centrality in the community interaction network to reveal the relative importance of the research area for knowledge transfer in the network over time. For example, all dynamic communities shown in Fig 5 are relatively long-lived and stable. However, the low centrality topics in Economics, Physics, and Medicine, remain isolated (degree 0, betweenness = 0), in the early portion of the dataset (2000–2010) as they represent later applications of XAI research and thus play no part in the knowledge transfer in the early period. In contrast, those research areas from the Computer Science, Statistics, and Psychology disciplines, such as ‘feature selection’, ‘regression’ and ‘association rule mining’, have consistently high betweenness centrality (0.1), suggesting that they engage in knowledge transfer consistently throughout the development of XAI research. Thus, we conclude these research areas to represent the methodological and theoretical foundations of XAI literature.

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Fig 5. Foundation research areas life-cycles.

Dynamic community life-cycles of the communities with the highest betweenness centrality (left) and lowest betweenness centrality (right) in the period 2000–2010. Each row represents the life-cycle of a dynamic community and each cell in the row is populated if that dynamic community appears in the network as a step community in the corresponding time step. Each cell is coloured to show the most common ASJC category among the papers in the step community.

https://doi.org/10.1371/journal.pone.0329302.g005

Secondly, we assess the extent to which contemporary research areas in XAI leverage knowledge and methodologies from foundational research in the field. We identify the contemporary research areas in the literature as dynamic communities where the average age of the papers is six years or fewer (i.e., published since 2017). We focus our analysis on large communities (greater than 50 papers), with a content stability score above the mean measured across the dataset. Thus, we consider large communities of recent research papers with coherent content/topic as the clearest representations of the contemporary research in the literature.

Finally, we assess how these research areas rely on foundational research using interactions in the community interaction network measured at the most recent time step (2023). Fig 6 reports the interaction (citation) probabilities (see Eq 2), between the largest contemporary research areas in the field and the foundations identified previously. For comparison, we include equivalent scores measured between the contemporary research topics and more recent central topics, corresponding to the dynamic communities with the highest betweenness centrality during 2020–2023. We find that knowledge transfer from methodological and theoretical foundations in XAI research to contemporary research areas is quite varied, with subjects like ‘disentangled representation learning’ and ‘hate-speech detection’ making many more references to the foundational topics (interaction probabilities 1%) compared to topics like ‘semantic segmentation’ or ‘saliency maps’ (interaction probabilities 0). Furthermore, we note that the methodological foundations like ‘data mining’ and ‘association rule mining’ receive more citations from contemporary topics than the theoretical or psychology-based foundations.

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Fig 6. Knowledge transfer between foundations of XAI and contemporary topics.

The percentage of total possible interactions (citations) between contemporary research areas in XAI literature and the foundation areas. For comparison, some recent central topics in XAI are included on the right. For readability, the interaction probabilities are scaled to percentages. For example, if 20% of papers in research area A cite 10% of papers in research area B, the resulting interactions score would be 2%. Community interaction probabilities are calculated according to Eq 2.

https://doi.org/10.1371/journal.pone.0329302.g006

In Fig 7, we highlight four subsets of the contemporary research areas which have similar content to compare how they interact with the established literature. In particular, we group research areas into four research topics relating to (i) fairness, (ii) natural language processing, (iii) computer vision, and (iv) adversarial machine learning. Thus, we reveal some patterns in knowledge transfer by topic. Overall, we find that research areas with similar content appear to engage in similar knowledge transfer patterns. For example, research areas within the ‘computer vision’ group exhibit similar knowledge transfer behaviour as they rely more on knowledge from the more recently central topics (interaction probabilities between 0.5%–1%), than they do from the historically central or ‘foundational’ topics (probabilities 0.1%). Similarly, research areas within the ‘adversarial machine learning’ topic all rely more on knowledge from the foundational literature than they do the more recently central topics. Conversely, research areas in the ‘fairness’ group demonstrate different knowledge transfer patterns despite their related content. In particular, the two research areas labelled ‘hate speech’ and ‘gender bias’ make fewer citations to methodological foundations of XAI research than the third research area (labelled ‘discrimination/fairness’).

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Fig 7. The percentage of total possible interactions (citations) between contemporary research areas in XAI literature and the foundation areas.

For comparison, some recent central topics in XAI are included on the right. For readability, the interaction probabilities are scaled to percentages. For example, if 20% of papers in research area A cite 10% of papers in research area B, the resulting interactions score would be 2%.

https://doi.org/10.1371/journal.pone.0329302.g007

Knowledge silos

We now illustrate the identification of knowledge silos, which represent the research areas that are most isolated from the perspective of knowledge transfer. Specifically, we identify knowledge silos as the communities with the least interactions with other communities in the community interaction network. Table 1 reports summary statistics for the five research areas with the lowest sum across all interaction probabilities in the final (most recent) snapshot of the community interaction network (snapshot 2023). During this process we exclude small research areas made up of 10 or fewer papers.

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Table 1. Knowledge silos.

https://doi.org/10.1371/journal.pone.0329302.t001

XAI applications in Environmental Sciences/Atmospheric Chemistry and Physics and COVID-19 diagnosis from chest CT images are identified as two of the most isolated research areas in the corpus, with respect to knowledge transfer. Each of these research areas represent intuitive applications of XAI and machine learning research to important real-world challenges. However, the isolated position of these areas in the community networks is problematic. In fact, recent studies have highlighted limitations to the utility of each of these applications in their respective domains [57, 58]. Specifically, Silva and Keller show that dependencies and strong correlations between features lead to model explanations that are inconsistent with process-level understanding [58]. Similarly, in their review of computer vision solutions for COVID-19 detection, Roberts at al. find that none of the solutions are clinically viable, due to important methodological flaws in the machine learning applications [57]. These cases represent examples of some of the practical issues with isolated research areas and limited knowledge transfer in interdisciplinary applications. They highlight that unrealised knowledge integration, either from the domain of the application (as in [58]), or from the domain of the methods (as in [57]), can lead to poorer outcomes in terms of the utility of the applications. In the following section, we demonstrate our methods for identifying knowledge gaps, which refer to pairs of communities that exhibit low levels of knowledge transfer despite pertaining to similar topics, or sharing similar knowledge sources or knowledge outputs.

Knowledge gaps

To identify potential knowledge gaps between research areas in the XAI literature, we modelled the expected knowledge transfer between communities based on their content similarity and proximity in the community interaction network. Pairs of communities exhibiting substantially lower interaction (citation) rates than predicted were flagged as having significant knowledge gaps. The model essentially captures the relationship between research areas’ content similarity and the similarity between their knowledge sources and knowledge outputs (the two independant variables), and their observed knowledge transfer behaviour (the dependant variable). By analysing the residuals, we identify those pairs of communities that demonstrate less knowledge transfer than we would expect based on their content and related work. This approach allows detecting gaps in knowledge flow that may arise due to disciplinary boundaries, insular reading and citation patterns, or lack of awareness of complementary work.

Table 2 highlights the four communities that most consistently demonstrate knowledge gaps (i.e., have the greatest total residual score across all possible research areas) and the research areas with which they have the most significant gaps. We recognise that the knowledge gaps identified can be categorised into two groups. (i) Between methodological research areas and potential applications (e.g. between counterfactual explanations and multiple research areas in computer vision or between contrastive explanations and research ares in natural language processing). (ii) Between two applied research areas studying the same or similar topics (e.g. computer vision for medical images). In the case of (ii), we identify a pair of very similar research areas – both related to computer vision for medical images – that are evolving in parallel, with minimal knowledge transfer between them. This highlights one of the key benefits of our proposed methods for delineating research areas from the perspective of knowledge transfer. While NLP-based methods for recognising research topics may (correctly) group these research areas into a single topic, it is important to acknowledge that they are distinct from one another when studying knowledge transfer. Thus, we observe the benefits of studying citation relations and article content in tandem. By considering both sources of information, we can identify gaps in the literature and help to expose researchers to relevant works that they may otherwise overlook.

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Table 2. Knowledge gaps.

https://doi.org/10.1371/journal.pone.0329302.t002