# Semantic Similarity Based on Taxonomies
## 2 Methods for Computing the Information Content of a Concept in a Taxonomy  
The notion of the information content (IC) of a concept to compute semantic similarity was introduced for the first time by [PERSON] [17]. Based on the standard argumentation of information theory, it is defined as the negative log of the likelihood of the concept (see Equation (A1) in Appendix A). This is an extensional, or corpus-based, method as the likelihood of a concept is computed as the relative frequency of that concept in a corpus of documents. Another extensional method is _annotation frequency IC_[18], which exploits the _inverse document frequency_ (_IDF_) of a concept in a corpus of textual resources [19]. In particular, in [18], this method is applied to annotation vectors, i.e., sets of concepts of a taxonomy that are used to semantically annotate digital resources. However, most of the methods in the literature for computing IC are intensional or intrinsic. In fact, they compute it by considering only the structure of the taxonomy and do not need external resources. Indeed, extensional methods require the analysis of documents whose dimensions are statistically significant. And this amount of textual resources is not always available, especially in the case of very specific application domains. Therefore, intensional methods aim at overcoming these limits and avoiding additional efforts by exploiting the sole topology of the taxonomy. In particular, intensional methods leverage the following features of the taxonomy (see Table 1, where the fundamental definitions are recalled):  
* The number of hyponyms of the concept, where the greater it is, the less the IC. This is due to the assumption that the more general a concept, the less its informativeness. This feature is used by _[PERSON] et al. IC_[20], _[PERSON] et al. IC_[21], and _[PERSON] and [PERSON] 2 IC_[22]. _[PERSON] et al. IC_[23] considers the hyponyms of the hypernyms of the concept, but the basic assumption continues to be applied. * The depth of the concept, where the greater it is, the greater the IC. Again, this is in line with the general assumption regarding the specificity of a concept and its informativeness. This feature is used by _[PERSON] et al. IC_[21] and _[PERSON] et al. IC_[24], who also consider the depth of the hyponyms, and _[PERSON] et al. IC_[25] and _[PERSON] et al. IC_[23], who also consider the depth of the hypernyms. * The number of the hypernyms of the concept, which again take into consideration the assumption above. In fact, the greater the number of the hypernyms, the greater the IC. This feature is used by _[PERSON] et al. IC_[25] and _[PERSON] et al. IC_[23], who consider the hypernyms of the hypernyms, and _[PERSON] and [PERSON] 1 IC_[26]. * The number of the leaves of the concept, where the greater it is, the less the IC. This is again in accordance with the general assumption that correlates the specificity of a concept with its informativeness. This feature is used by _[PERSON] and [PERSON] 2 IC_[22] and _[PERSON] et al. IC_[25]. * The number of siblings of the concept, where the greater it is, the greater the IC. Here, the underlying assumption is that the greater the number of siblings of a concept, the greater its peculiarity and its informativeness, too. This assumption is exploited in the _top down IC_ found in [27] and by _[PERSON] and [PERSON] IC_[28]. However, in the latter, the siblings of hypernyms are also considered. In general, the number of hyponyms and the number of hypernyms of a concept are normalized by the total number of the concepts in the taxonomy, whereas the depth of the concept is normalized by the height of the whole taxonomy. The main features of the above recalled methods are summarized in Table 2.  
Additional methods for computing the IC of concepts are, for instance, the ones proposed in [29], which exploits not only the _is-a_ relationship but also the synonymy and polysemy contained in semantic structures such as WordNet, and in [30], which computes the IC of events in a process model.