# Understanding Query Combination Behavior in Exploratory Searches
## 4 Characterizing Query Combination Behavior
### Query Characteristics  
The most obvious factors to distinguish between QCB types may be the characteristics of queries. Therefore, we examined several different aspects of queries in QCB sessions, as follows:  
Average Semantic Distance of Queries: Semantic distance between CPQs may be a factor distinguishing the \"relation discovery category\" from all other QCB categories. To examine this, we measured the average similarity distance between CPQs in each QCB session for each QCB type. We measure semantic distance between queries based on CLSM (convolutional latent semantic model), presented by [PERSON] [40,41], which can generate a continuous semantic vector representation for each query string. The semantic distance between any two CPQs is calculated as the cosine similarity between their vectors in that semantic space, which is computed as Equation (1), as follows:  
\[Sim\big{(}CPQ_{i},CPQ_{j}\big{)}=\cos{in}\big{(}v_{i},v_{j}\big{)}=\frac{v_{i }^{T}v_{j}}{||v_{i}||||v_{j}||} \tag{1}\]  
\(v_{i}\) and \(v_{j}\) are the semantic vectors of \(CPQ_{i}\) and \(CPQ_{j}\). A semantic distance value of one indicates QCB with perfect same semantics. On the contrary, a semantic distance value of zero indicates that the semantic between QCB is completely unrelated. Figure 5 shows the average semantic distances between all CPQ in every QCB session for each QCB pattern. We notice from the figure that the average semantic distance of CPQ seemed to be a factor to distinguish between QCB patterns except for distinguishing between dominative query first pattern and topic specialization query first pattern. This can be explained by the analysis, where we discussed that the difference between dominative query first pattern and topic specialization query first pattern is the time sequence between dominative queries and topic specialization queries. The differences (other than the difference between dominative query first pattern and topic specialization query first pattern) between QCB patterns were statically significant at the 0.05 level, according to the two-tailed \(t\)-test and variance analyses. Subtask Belonging to Queries: In addition, we also considered the subtask belonging to the queries. Exploratory search tasks often tend to have multiple subtasks associated with them [42,43]. As we discussed, a given CPQ in a QCB session which was judged into the topic specialization category may be more likely to belong to the same subtask. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Reason** & \\ \hline Top 1 & Explored wrong search object in topic. & 54\% \\ Top 2 & The search results of CBQ and CPQ are same. & 17\% \\ Top 3 & Invalid combinations. & 11\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Top three mentioned reasons that make QCB fail. To examine this, we considered the Bayesian rose tree (BRT) model, proposed by [PERSON] and [PERSON], which has been proved to be one of the most advantageous techniques for searching subtask clustering [44]. Figure 6 shows the distribution of subtask belonging for each QCB pattern. A value of one indicates that all CPQs in every QCB session fell into the same search subtasks, while a value of zero indicates that each CPQ in every QCB session fell into different search subtasks. We notice from the figure that CPQs in the topic specialization QCB sessions are more likely in the same subtasks (more than 82%), which aligns with our previous observation. In addition, the CPQ in the relation discovery category is more likely in the same subtasks than that in the query diversification category. The differences between patterns in each QCB category were not statistically significant at the 0.05 level according to the two-tailed \(t\)-test and the variance analysis, suggesting that this was unlikely to be a distinguishing factor. However, the differences between categories were statistically significant at the 0.05 level according to a two-tailed \(t\)-test  
Figure 5: Average semantic distances between all CPQs in every QCB session for each QCB pattern.