## 3 Development of ICRT
### Clustering of IITs and Involving Articles  
As an IIT between two articles contains those terms that indicate the shared issue of the two articles, issue-based clustering of articles can be done by clustering the IITs. Therefore, with IBS and IIT defined for any two articles (ref. Equations (8) and (14) defined above), ICRT conducts issue-based clustering of articles by clustering the IITs (ref. Figure 1(c) noted above). ICRT is designed to work as a post-processor of existing clustering systems, which provides clustering results to be refined by ICRT. The algorithm is outlined in Figure 3.  
Given _PreClusters_ as the set of clusters produced by an underlying clustering system, ICRT refines _PreClusters_ by identifying and clustering the IITs of all pairs of articles in _PreClusters_ (see Steps 1 to 4 in Figure 3). An IIT between two articles actually corresponds to a cluster of the two articles; hence, given two articles, _a1_ and _a2_ (in a cluster in _PreClusters_), an initial cluster \(c\) can be constructed and represented as _<c1 BS_(_c_), _clTT_(_c_), _ArticlePair_(_c_)>, where _clBS_(_c_) is the cluster IBS for \(c\) initially set to IBS(_a1,a2_); _clTT_(_c_) is the cluster IIT for \(c\) initially set IIT(_a1,a2_); and _ArticlePair_(_c_) is the set of involving article pairs in \(c\), and hence, is initially set to _{_<a1,a2>_} (see Step 2 in Figure 2).  
ICRT then ranks all clusters according to their _c1 BS_ values (see Step 3 in Figure 3), and tries to group any two clusters. Those clusters that have higher _clBS_ values have a higher priority to be grouped with other clusters (see Step 4 in Figure 3). Two clusters _c1_ and _c2_ can be grouped to form a new cluster if four conditions are satisfied: (1) articles in _c1_ and _c2_ are grouped in a cluster in _PreClusters_ as well; (2) _clBS_(_c1_) and _clBS_(_c2_) are not less than 0.5; (3) sum of _IDF_ values of intersecting terms in _clTT_(_c1_) and _clTT_(_c_2_) is not less than a threshold (tuned by training data); and (4) an article pair _<a1,a2>_ exists whose IBS is not less than 0.5, and _a1_ (_a2_) is an article in _c1_ (_c2_) but not in _c2_ (_c1_). For a new cluster \(c\) produced by grouping _c1_ and _c2_ (_clBS_(_c1_) > _clBS_(_c2_)), _clBS_(_c_) is the average IBS of all article pairs in _ArticlePair_(_c_) and _ArticlePair_(_c_2_); _clTT_(_c_) is composed of intersecting terms in _clTT_(_c1_) and  
Figure 3: The algorithm to cluster _articles_ by clustering _IITs_.  
_cIIT(c2)_; and _ArticlePair(c)_ is the union of _ArticlePair(c1)_ and _ArticlePair(c2)_ (see Step 4.1.2.1 in Figure 3). Cluster _c1_ is then replaced with the new cluster \(c\), and _c2_ is removed (see Steps 4.1.2.2 and 4.1.2.3 in Figure 3) so that \(c\) may be further grouped with other clusters.  
To further refine the clustering results, ICRT continues to consider potential clusters of articles that have high IBS values (see Steps 5 to 7 in Figure 3). A pair of articles that are not grouped into a cluster in _PreClusters_ can be a _potential_ cluster if IBS between the two articles is not less than 0.5 (see Step 5 in Figure 3). By adding these potential clusters into the clustering results, ICRT can consider those clusters that are not identified by the underlying clustering system. ICRT re-ranks the clusters according to their corresponding _clBS_ values (see Step 6 in Figure 3), and triggers the same clustering procedure noted above (Step 4 and Step 7 in Figure 3 are basically the same), except that two clusters _c1_ and _c2_ can be grouped to form a new cluster if the 2 nd to the 4 th conditions noted above are satisfied (i.e., the 1 st condition is not considered, as ICRT is now considering those clusters that are _not_ in _PreClusters_).  
After the above two clustering processes, the clusters are re-ranked again (according to their _IBS_ values), and the articles in each cluster are retuned as a ranked list of article clusters (see Steps 8 and 9 in Figure 3). If the user sets a fixed number K of resulting clusters, only top-K clusters are returned.