# Semantic Similarity Based on Taxonomies
## 4 Methods for Computing Semantic Similarity between Sets of Concepts  
In the literature, traditionally, the semantic similarity between sets of concepts is evaluated according to the well-known Tversky model [37], such as Dice [50], Jaccard [51], and Sigmoid [52], just to mention a few. However, these are set-theoretic methods that are not addressed in this review as they do not rely on a given taxonomy of concepts. With regard to the taxonomy-based similarity measures, in this section, we recall five \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & **Depth** & **Height** & **len** & **lcs** & **Hypo** & **Hyper** & **IC** & **Further Info** \\ \hline \(sim_{radk}\)[41] & 1989 & & & X & & & & & distance \\ \(sim_{n\&bp}\)[42] & 1994 & X & & X & X & & & & \\ \(sim_{lrs}\)[17] & 1995 & & & & & X & X & Resnik [17] \\ \(sim_{lsc}\)[34] & 1997 & & & & & X & & Resnik [17] \\ \(sim_{lsc}\)[43] & 1998 & & X & X & & & & & \\ \(sim_{lsin}\)[35] & 1998 & & & & X & & & Resnik [17] \\ \(sim_{lsin}\)[49] & 2006 & X & & & X & X & & & \\ \(sim_{almuubai}\)[45] & 2006 & X & X & X & X & & & \\ \(sim_{p\&bs}\)[36] & 2009 & & & & & X & Seco et al. [20] \\ \(sim_{m\&2}\)[24] & 2012 & & & X & X & Seco et al. [20] & tuning param. \\ \(sim_{l\&f\&f}\)[46] & 2014 & X & & & X & & \\ \(sim_{npath}\)[38] & 2017 & & & X & X & Resnik [17] & tuning param. \\ \(sim_{zhang\_1}\)[33] & 2018 & & & & X & & Zhang 1 et al. [33] & \\ \(sim_{zhang\_2}\)[47] & 2018 & & & & X & X & & \\ \(sim_{D_{k}}\)[39] & 2021 & & & & & & any & tuning param. \\  & & & & & & & words senses \\ \(sim_{HSS}\)[40] & 2022 & & & X & X & [PERSON] [17] & words senses \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Methods for computing the semantic similarity between concepts in a taxonomy. methods: the _WNSim similarity_[53], the measures introduced by [PERSON] and [PERSON] [46], [PERSON] et al. [54], and [PERSON] et al. [55], and the _SemSim\({}^{p}\) similarity_[18]. Let an annotation vector, \(av\), be a set of concepts from the taxonomy \(T=(C,E)\), defined as \(av=(c_{1},..,c_{n}),c_{i}\in C,i=1,..,n\). In the following, let \(av_{1}\), \(av_{2}\) be two annotation vectors from the taxonomy \(T=(C,E)\). * _WNSim similarity_[53] is a method for computing semantic similarity between sets of concepts representing sentences in documents, which leverages the Leacock and Chodorow similarity \(sim_{l\&c}\)[43] defined in the previous section (see Equation (17)): \[SIM_{WN}(av_{1},av_{2})=\frac{\sum_{c_{i}\in av_{1}}max_{c_{j}\in av_{2}}( sim_{l\&c}(c_{i},c_{j}))*IDF(c_{i})}{\sum_{c_{i}\in av_{1}}IDF(c_{i})}.\] (17)
* _Rezaei and [PERSON] similarity_[46] is a similarity measure between sets of concepts based on matching the individual concepts of the sets by applying the \(sim_{r\&f}\) defined above (see Equation (15)): \[SIM_{R\&F}(av_{1},av_{2})=\frac{\sum_{c_{i}\in av_{1}}sim_{r\&f}(c_{i},c_{j} )}{|av_{1}|}\] (18) where \(|av_{1}|\) is the cardinality of the set \(av_{1}\). * _[PERSON] et al. similarity_[54] computes the similarity of pairs of concepts belonging to different sets by using the method proposed by [PERSON] et al. \(sim_{li}\) recalled above, which combines the shortest path length between the concepts and the depths of their subsumers in the taxonomy non-linearly (see Equation (19)): \[SIM_{[PERSON]}(av_{1},av_{2})=\frac{1}{|av_{1}|}\sum_{c_{i}\in av_{1}}max_{c_{j} \in av_{2}}S(c_{i},c_{j})\] (19) where \(|av_{1}|\) is the cardinality of the set \(av_{1}\), and \[S(c_{i},c_{j})=\left\{ \begin{array}{ll}sim_{li}(c_{i},c_{j})&\text{ if }c_{i}\
eq c_{j}\\ 1&\text{ otherwise.}\end{array} \right.\]
* _[PERSON] et al. similarity_[55] computes the similarity between two sets of concepts \(av_{1}\) and \(av_{2}\) by considering, for each pair of concepts, one from \(av_{1}\) and one from \(av_{2}\), the IC of their \(lcs\) (see Equation (20)): \[SIM_{Wang}(av_{1},av_{2})=\frac{1}{|av_{1}|*|av_{2}|}\sum_{c_{i}\in av_{1}} \sum_{c_{j}\in av_{2}}ic(lcs(c_{i},c_{j}))\] (20) where the IC is computed according to the Resnik IC (see Section 2).