# Semantic Similarity Based on Taxonomies
## Appendix A Formulas of Methods for Computing the IC of Concepts in a Taxonomy  
Here, we report the formulas for computing the IC of a concept \(c\) in a taxonomy \(T=(C,E)\) according to the methods discussed in Section 2 (see definitions in Table 1).  
* _Resnik IC_[17] \[ic_{resnik}(c)=-log\bigg{(}\frac{freq(c)}{|C|}\bigg{)}\] (1) where, \(freq(c)\) is the relative frequency of the concept \(c\) in a corpus of text documents.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Correlation with HJ** & **Degree of Confidence** \\ \hline _WNSim similarity_ & 0.61 & 84.33\% \\ _[PERSON] and [PERSON] similarity_ & 0.46 & 74.73\% \\ _[PERSON] et al. similarity_ & **0.69** & 77.89\% \\ _[PERSON] et al. similarity_ & 0.04 & 74.09\% \\ _SemSim\({}^{p}\) similarity_ & **0.69** & **85.67**\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Methods for computing semantic similarity between sets of concepts: experimental results.  
* _[PERSON] et al. IC_[20] \[ic_{scco}(c)=1-\frac{log(|hypo(c)|+1)}{log(|C|)}.\] (A2)
* _[PERSON] et al. IC_[21] \[ic_{zhou}(c)=k*\left(1-\frac{log(|hypo(c)|+1)}{log(|C|)}\right)+(1-k)*\frac{ log(depth(c))}{log(height(T))}.\] (A3)
* _Sebti and Barfroush IC_[28] \[ic_{sebti}(c)=-log\left(\prod_{c_{i}\in hyper(c)\cup\{c\}}\frac{1}{|silbing(c_ {i})|}\right).\] (A4)
* _[PERSON] et al. IC_[31] \[ic_{meng}(c)=\frac{log(depth(c))}{log(height(T))}*\left(1-\frac{log(\sum_{c^{ \prime}\in hypo(c)}\frac{1}{depth(c^{\prime})}+1)}{log(|C|)}\right).\] (A5)
* _Sanchez and Batet 1 IC_[26] \[ic_{skb\_1}(c)=-log\left(\frac{commonness(c)}{commonness(root)}\right)\] (A6) where \[commonness(c)=\begin{cases}\frac{1}{|hyper(c)|},&\text{if $c$ is a leaf}\\ \sum_{c^{\prime}\in\text{leaves}(c)}\frac{1}{|hyper(c^{\prime})|},&\text{ otherwise.}\end{cases}\] (A7)
* _Sanchez and Batet 2 IC_[22] \[ic_{skb\_2}(c)=-log\left(\frac{\frac{|lares(c)|}{|hypo(c)|}+1}{|leaves(T)|+1}\right).\] (A8)
* _Top Down IC_[27] \[ic_{td}(c)=log(|silbings(c)|+1)-ic_{td}(directHyper(c))\] (A9) where \(ic_{td}(root)\) is assumed to be equal to 0, and \(T\) is a tree-shaped taxonomy.
* _[PERSON] et al. IC_[25] \[ic_{yuan}=\frac{log(depth(c))}{log(height(T))}*\left(1-\frac{log(|leaves(c)|+ 1)}{log(leaves(T)+1)}\right)*\left(1-\frac{log(|hyper(c)|+1)}{log(|C|)} \right).\] (A10)
* _[PERSON] et al. IC_[23] \[ic_{taieb}=\left(\sum_{c_{i}\in hyper(c)}score(c_{i})\right)*avgdepth(c)\] (A11) where \[score(c_{i})=\left(\sum_{c_{j}\in directHyper(c_{i})}\frac{depth(c_{j})}{| hypo(c_{j})|}\right)*|hypo(c_{i})|\] and \[avgdepth(c)=\frac{1}{|hyper(c)|}\sum_{c\in hyper(c)}depth(c).\]* _[PERSON] et al. IC_ [32]  
\[\begin{split} ic_{\text{adhikari}}(c)=\frac{log(depth(c)+1)}{log( height(T)+1)}*\left(1-log\left(\frac{\frac{leaves(c)*|directHyper(c)|}{leaves(T)}}{|hyper(c)|}+1 \right)\right)*\\ \left(1-\frac{log\left(\sum_{i\in\mathit{hypp}(c)}\frac{1}{depth (i)}+1\right)}{log(|C|)}\right).\end{split} \tag{12}\]
* _[PERSON] et al. 1 IC_ [33]  
\[\begin{split} ic_{\text{zhang\_1}}=-(1-k)*\frac{1}{n}*\sum_{i=1}^{ n}log\left(\prod_{c_{i}\in\mathit{hyper}(c)}\frac{1}{siblings(c_{i})}+1 \right)+k*\left(1-\frac{log(|\mathit{hypp}(c)|+1)}{log(|C|)}\right)\\ \text{where}\\ k=\frac{|\mathit{hypp}(c)|}{\mathit{hyper}(c)+\mathit{hypp}(c)}\\ \text{and}\\ n=|\mathit{directHyper}(c)|.\end{split} \tag{13}\]
* _Annotation Frequency IC_ [18]  
\[ic_{\text{af}}(c)=-IDF(c). \tag{14}\]