# Semantic Similarity Based on Taxonomies
## 3 Methods for Computing Semantic Similarity between Concepts
### Information Content-Based Methods  
To compute the similarity between concepts in a taxonomy, a substantial group of methods relies on the IC of concepts. They are briefly described in the following. * _[PERSON] similarity_ (\(sim_{res}\)) [17] (see Equation (1)), which assumes that the more information two concepts share, the more similar they are. Then, the information shared by two concepts is provided by the IC of the concepts that subsume them in the taxonomy: \[sim_{res}(c_{1},c_{2})=max_{c_{i}\in hyper(c_{1})\cap hyper(c_{2})}ic(c_{i})\] (1) where the maximum value is obtained for \(c_{i}\) is one of the \(lcs(c_{1},c_{2})\). * _[PERSON] and [PERSON] similarity_ (\(sim_{j\&c}\)) [34] (see Equation (2)), which depends on the IC of three nodes in the taxonomy, i.e, the two compared concepts, and their least common subsumer: \[sim_{j\&c}(c_{1},c_{2})=\frac{1}{ic(c_{1})+ic(c_{2})-2*ic(lcs(c_{1},c_{2}))}.\] (2)
* _[PERSON] similarity_ (\(sim_{lin}\)) [35] (see Equation (3)), which, analogously to [34], is based on the ICs of the two compared concepts and their _lcs_: \[sim_{lin}(c_{1},c_{2})=\frac{2*ic(lcs(c_{1},c_{2}))}{ic(c_{1})+ic(c_{2})}.\] (3) \begin{table}
\begin{tabular}{l l l} \hline \hline
**Method** & **Year** & **Features** \\ \hline _Resnik IC_[17] & 1995 & Frequency of \(c\) in a corpus of documents \\ _[PERSON] et al. IC_[20] & 2004 & Hyponyms of \(c\) \\ _[PERSON] et al. IC_[21] & 2008 & Hyponyms and depth of \(c\), and height of \(T\), and tuning parameter \\ _Sebti and Barfroush IC_[28] & 2008 & Siblings of \(c\) and of its hypernyms \\ _[PERSON] et al. IC_[31] & 2012 & Depth of \(c\) and of its hyponyms, and height of \(T\) \\ _[PERSON] and Batet 1 IC_[26] & 2012 & Hypernyms of \(c\) and of its leaves \\ _[PERSON] and [PERSON] 2 IC_[22] & 2013 & Hyponyms and leaves of \(c\), and leaves of \(T\) \\ _Top Down IC_[27] & 2013 & Direct hypernyms and siblings of \(c\) \\ _[PERSON] et al. IC_[25] & 2013 & Hypernyms, depth, and leaves of \(c\), and height and leaves of \(T\) \\ _[PERSON] et al. IC_[23] & 2014 & Hypernyms and depth of \(c\), hyponyms, and depth of the hypernyms \\ _[PERSON] et al. IC_[32] & 2015 & Depth, leaves and hypernyms of \(c\), depth of hyponyms of \(c\), height and leaves of \(T\) \\ _[PERSON] et al. IC_[33] & 2018 & Hypernyms and hyponyms of \(c\), siblings of hypernyms of \(c\) \\ _Annotation Frequency IC_[18] & 2023 & _ID_ of \(c\) in a corpus of documents \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Methods for computing the IC of a concept \(c\) in a taxonomy. * _P&S similarity_ (\(sim_{P\&S}\)) [36], inspired by [PERSON]'s set-theoretic formulation of similarity [37], which is based on both the ICs of the two compared concepts and the one of their _lcs_ (see Equation (4)): \[sim_{P\&S}(c_{1},c_{2})=3*ic(lcs(c_{1},c_{2}))-ic(c_{1})-ic(c_{2}).\] (4)
* _[PERSON] and Zhou similarity_[24], based on the IC and shortest path length, as shown in Equation (5): \[sim_{m\&z}(c_{1},c_{2})=\left(\frac{2*ic(lcs(c_{1},c_{2}))}{ic(c_{1})+ic(c_{2} )}\right)\left(\frac{1-c^{-k\cdot len(c_{1},c_{2})}}{c^{-k\cdot len(c_{1},c_{2 })}}\right)\] (5) where \(k\) is a factor, which is manually computed to improve the performance of the method. * _wpath similarity_ (\(sim_{wpath}\)) [38], defined in terms of the shortest path distance between the compared concepts and the ICs of their _lcs_ (see Equation (6)): \[sim_{wpath}(c_{1},c_{2})=\frac{1}{1+len(c_{i},c_{j})*k^{ic(lcs(c))}}\] (6) where \(k\) is the parameter that weighs the contribution of the IC of the _lcs_. * _Zhang 1 similarity_ (\(sim_{zhang\_1}\)) [33] (see Equation (7)), which uses the Lin similarity [35], as expressed by the argument of the logarithm function. However, differently from [PERSON], [PERSON]'s similarity, in its original version, it adopts the work of _[PERSON] et al.