## 3 Development of BCCCC  
The main ideas of BCCCC are illustrated in Figure 1, which also highlights main ideas of BC and its two variants IBS (Issue-Based Similarity [9]) and DBC (DescriptiveBC [10]). BC estimates the similarity between two articles \(a_{1}\) and \(a_{2}\) by considering whether they cite the _same references_, i.e., Type I similarity in Figure 1. For example, in Figure 1, \(r_{1m}\) cited by \(a_{1}\) is simply \(r_{23}\) cited by \(a_{2}\), and hence BC may increase the similarity between \(a_{1}\) and \(a_{2}\). Both IBS and DBC estimate the similarity by considering how \(a_{1}\) and \(a_{2}\) cite _references with similar titles_, i.e., Type II similarity in Figure 1. For example, in Figure 1, \(r_{13}\) (cited by \(a_{1}\)) and \(r_{22}\) (cited by \(a_{2}\)) have similar titles (even though they are different references), and hence IBS and DBC may increase the similarity between \(a_{1}\) and \(a_{2}\). In addition to the above two types of similarity (i.e., Type I and Type II), BCCCC also considers how \(a_{1}\) and \(a_{2}\) cite those references that are cited by articles in the same _categories_ (i.e., Type III similarity, which is measured by category-based CC). For example, in Figure 1, \(r_{11}\) (cited by \(a_{1}\)) and \(r_{21}\) (cited by \(a_{2}\)) are cited by two articles in the same category (even though the two citing articles are different articles), and hence BCCCC may increase the similarity between \(a_{1}\) and \(a_{2}\). More specifically, the similarity between two references \(r_{1}\) and \(r_{2}\) is composed of two parts: (1) text-based similarity (for Type I similarity and Type II similarity noted above); and (2) citation-based similarity (for Type III similarity noted above). Equation (2) defines the text-based similarity, which is 1.0 if \(r_{1}\) and \(r_{2}\) are the same reference; otherwise it is estimated based on the percentage of the terms shared by titles of \(r_{1}\) and \(r_{2}\). When computing the percentage of the shared terms, each term has a weight measured by its IDF (inverse document frequency, see Equation (3). IDF of a term \(t\) measures how _rarely_\(t\) appears in the titles of the references of articles. If fewer articles with references mentioning \(t\) in their titles, \(t\) will get a larger IDF value. Two references will have larger text-based similarity if their titles share many terms with larger IDF values. Figure 1: Main ideas of Bibliographic Coupling with Category-based Cocitation (BCCCC), which is a version of BC enhanced by considering three types of similarity (Type I to Type III), including the one based on _category-based_ CC (i.e., Type III). \[TextSim_{ref}(r1,r2)=\left\{ \begin{array}{l}1,if\ r1=r2;\\ \frac{\sum\limits_{\begin{subarray}{c}t\in T\text{\emph{Int}}(r1)\cap\text{ \emph{Int}}(r2)\\ t\in T\text{\emph{Int}}(r1)\cap\text{\emph{Int}}(r2)\\ \end{subarray}}IDF(t)\\ \end{array} },\text{\emph{otherwise.}}\right. \tag{2}\]  
\[IDF(t)\ =Log_{2}\frac{Total\ number\ of\ articles+0.5}{Number\ of\ articles\ whose\ references\ mention\ t\ in\ their\ titles+0.5} \tag{3}\]  
The citation-based similarity between two references \(r_{1}\) and \(r_{2}\) is defined in Equation (4), where _CategorySpaceVec_ is a vector with \(C\) dimensions (\(C\) is the number of categories), and _CosineSim_ is the cosine similarity between two vectors (i.e., cosine of the angle of the two vectors). Each dimension in _CategorySpaceVec(r)_ corresponds to a category, and the value on the dimension is the number of articles (in the category) that cite \(r\). Therefore, references \(r_{1}\) and \(r_{2}\) will have large citation-based similarity if they are cited by articles in a similar set of categories. In that case, \(r_{1}\) and \(r_{2}\) are actually cited by articles with a similar set of research focuses, and hence may be related to each other.