## 2 Background
### Citation-Based Similarity Measures  
Many similarity measures worked on citations among articles, including in-link citations and out-link citations. For an article \(a\), in-link citations are those articles that cite \(a\), while out-link citations are those articles that \(a\) cites. Some techniques treated the citations as undirected and unweighted links in a graph on which article clusters were produced (a survey and comparison of these techniques can be found in [8]). These techniques thus clustered articles by analyzing the inter-connections among articles, rather than similarity between articles, which is employed by ICRT and many text clustering techniques.  
_Co-citation_ is a representative technique that considers in-link citations to estimate inter-article similarity [9]. Two articles may be related to each other if they are co-cited by other articles. Clustering techniques based on co-citation has been developed and applied to various domains (e.g., patent analysis [10]). However, applicability of the techniques based on in-link citations is limited, as many scholarly articles have very few (or even no) in-link citations. ICRT works on out-link citations of scholarly articles, which are more publicly available, even for newly-published articles that have not yet received any in-link citations.  
_Bibliographic_ coupling (BC) is a representative technique that considers out-link citations [11], which were found to be more helpful than in-link citations in the classification [12] and clustering [13] of scholarly articles. BC was also a typical citation-based similarity measure that was integrated with content-based similarity measures by hybrid measures [12; 13; 14; 15]. The hybrid measures did not always perform significantly better than BC [12], and they even performed significantly worse on occasion [16]. Equation (1) is a typical way to estimate BC similarity between two articles, \(a1\) and \(a2\)[12], where O\({}_{a1}\) and O\({}_{a2}\) are the sets of articles that \(a1\) and \(a2\) cite respectively. When both O\({}_{a1}\) and O\({}_{a2}\) are empty, the similarity is set to 0.  
\[BC(a1,a2)=\frac{|O_{a1}\cap O_{a2}|}{|O_{a1}\cup O_{a2}|} \tag{1}\]  
BC has a weakness in dealing with two articles that are related but cite different references, and hence, the similarity measure, _DescriptiveBC_, was proposed to employ titles of the references to tackle the weakness [16], as different but related references may share certain key terms in their titles. As defined in Equation (2), Jaccard index is employed to estimate similarity between titles of two references \(r1\) and \(r2\) (where _Title_(\(r\)) is the set of terms in the title of a reference \(r\)), and the _DescriptiveBC_ similarity between two articles \(a1\) and \(a2\) is defined in Equation (3), where \(R_{a}\) is the set of references in article \(a\).  
\[Sim_{ref}(r1,r2)=\left\{\begin{array}{l}1,\,if\,r1=r2;\\ \frac{|Title(r1)\cap Title(r2)|}{|Title(r1)\cap Title(r2)|},otherwise.\end{array}\right. \tag{2}\]  
\[DescriptiveBC(a1,a2)=\frac{\sum\limits_{r1\in R_{a1}}Max_{2\in R_{a2}}Sim_{ ref}(r1,r2))+\sum\limits_{r2\in R_{a2}}Max_{r1\in R_{a1}}Sim_{ref}(r1,r2))}{|R_{a1}|+|R_{a2}|} \tag{3}\]  
However, these similarity measures did not aim at _issue-based clustering_. They did not estimate issue-based similarity; rather, they estimated the similarity between two articles based on _all_ reference titles in the article, without considering the common case where these references are about different issues. As an article may discuss multiple issues, two articles may be in a cluster if they discuss an issue, even though they are not entirely similar to each other overall; and conversely, three articles should _not_ be in a cluster if they discuss different issues, even though they are similar to each other _overall_. ICRT is thus composed of two novel components for (1) estimation of issue-based similarity, and (2) clustering of scholarly articles based on the issue-based similarity.