# Semantic Similarity Based on Taxonomies
## 3 Methods for Computing Semantic Similarity between Concepts
### Non-Information Content-Based Methods  
* \(len(c_{1},c_{1})=0\) (zero property);
- \(len(c_{1},c_{2})=len(c_{2},c_{1})\) (symmetric property);
- \(len(c_{1},c_{2})\geq 0\) (positive property);
- \(len(c_{1},c_{2})+len(c_{2},c_{3})\geq len(c_{1},c_{3})\) (triangular inequality). However, in general, symmetry and triangular inequality are not satisfied by semantic similarity.
* _[PERSON] and [PERSON] similarity_[42] is based on the depth of the least common subsumer of the concepts and the conceptual distance of the concepts from it, as defined by Equation (11): \[sim_{wkp}(c_{1},c_{2})=\frac{2*depth(lcs(c_{1},c_{2}))}{len(c_{1},lcs(c_{1},c _{2}))+len(c_{2},lcs(c_{1},c_{2}))+2*depth(lcs(c_{1},c_{2}))}.\] (11)
* _[PERSON] and [PERSON] similarity_[43] is based on the shortest path between the two concepts. It also considers the maximum depth of the taxonomy \(T\), i.e., its height, as in Equation (12) \[sim_{l\&c}(c_{1},c_{2})=-log\bigg{(}\frac{len(c_{1},c_{2})}{2*height(T)} \bigg{)}.\] (12)
* _Li similarity_ (\(sim_{li}\)) [44] is based on the shortest path distance between the compared concepts and the depth of their \(lcs\), according to Equation (13) \[sim_{li}(c_{1},c_{2})=e^{\alpha*len(c_{1},c_{2})}*\frac{e^{\beta*depth(lcs(c_ {1},c_{2}))}-e^{-\beta*depth(lcs(c_{1},c_{2}))}}{e^{\beta*depth(lcs(c_{1},c_ {2}))}+e^{-\beta*depth(lcs(c_{1},c_{2}))}}\] (13) where \(e\) is Euler's number, and \(\alpha\), \(\beta\) are parameters that contribute to the path length and depth, respectively. According to the experiment in [44], the empirical optimal parameters are \(\alpha=0.2\) and \(\beta=0.6\).
* _Al-Mubaid similarity_[45] (see Equation (14)) is based on the height of the taxonomy, the depth of the \(lcs\), and the shortest path length: \[sim_{alumbaid}(c_{1},c_{2})=log((len(c_{1},c_{2})-1)^{*}*(CSpec(c_{1},c_{2})^{ \beta}+k)\] (14) where \(CSpec(c_{1},c_{2})=height(T)-depth(lcs(c_{1},c_{2}))\), \(\alpha\), \(\beta>0\), and \(k\geq 0\) (in their experiments \(k=1\)).
* _[PERSON] and [PERSON] similarity_[46] is based on the depth of the compared concepts and of their \(lcs\), as shown in Equation (15): \[sim_{r\&f}(c_{1},c_{2})=\frac{2*depth(lcs(c_{1},c_{2}))}{depth(c_{1})+depth (c_{2})}\] (15) which, in a tree-shaped taxonomy coincides, with the [PERSON] and [PERSON] similarity (see Equation (11)).  
* _Zhang 2 similarity_[47] is based on the hyponyms of the concepts and their \(lcs\), i.e., the _desc_ function according to the notation above. In particular, such a measure is computed according to Equation (16): \[sim_{zhang\_2}(c_{1},c_{2})=\frac{2*log(|C|)-log(|hypo(lcs(c_{1},c_{2}))|+1)}{2* log(|C|)-log(|hypo(c_{1})|+1)-log(|hypo(c_{2})|+1)}.\] (16)  
Furthermore, the method proposed in [48] relies on the Wikipedia Category Graph (WCG), a hierarchical knowledge structure used to categorize Wikipedia articles. However, the WCG is not a proper taxonomy as it is built by volunteers who link the categories without explicitly specifying the nature of the relation. For this reason, the method is not considered in this review.  
Table 3 recaps the main features of the recalled proposals and the methods they use for computing the IC that are described in detail in Section 6.