# A Purely Entity-Based Semantic Search Approach for Document Retrieval
## 3 Materials and Methods
### Entity Linking Method
#### 3.1.4 Disambiguation  
The disambiguation task is achieved using a graph-based algorithm, which is the central part of our EL4 DT method. The constructed graph is a weighted graph G = (V, E), where the node set V contains all the selected candidate entities from a given paragraph, and each edge represents the semantic relationship between two entities. The main goal of the disambiguation algorithm is to select among the ambiguated entities (entities with weak scores) only those related to sure entities (entities with scores higher than or equal to 0.5). Thus, other weak entities are ignored. Furthermore, EL4 DT identifies the best cluster, the group of related entities with the higher score among other clusters in the graph. In other words, the best cluster in the graph is supposed to be the paragraph's main idea. In a graph, we note that a cluster is a set of entities connected by edges whose weights are greater than zero.  
The set of entities in a paragraph is expressed by \(E_{p}=\{e_{1},e_{2},....,\,e_{n}\}\), where n represents the number of entities in the paragraph.  
The \(E_{coh}\) symbol stands for coherence entities (document entity coherence), which exist in the document title and the document's strong entities. The strong entity concept refers to entities annotated by EL4 DT with an annotation score higher than or equal to 0.85. Thus, \(E_{coh}\) represents the intersection between the document's strong entities \(SE_{d}\) and the document's title entities \(E_{dt}\), as Equation (1) shows.  
\[E_{coh}=E_{dt}\bigcap SE_{d} \tag{1}\]  
After the graph initialization step, the graph scoring expression is based on Equation (2), which shows how the graph edges are scored:  
\[GS\big{(}e_{i},e_{j}\big{)}=\frac{rScore\big{(}e_{i},e_{j}\big{)}\times\big{(} LScore(e_{i})+LScore\big{(}e_{j}\big{)}\big{)}}{\big{|}E_{p}\big{|}} \tag{2}\]  
where rScore\(\big{(}e_{i},e_{j}\big{)}\) gives the number of relationships between two entities, as computed by Equation (3), where the R symbol represents the different types of relationships between the two entities. Moreover, the relationship between the two entities is either direct or indirect. Direct relationships exist when entities share the common article categories of DBpedia. Moreover, from the SKOS of DBpedia, there are some relationships between entities such as the <skos:broader> and <skos:related> predicates. However, an indirect relationship means that \(e_{i}\) and \(e_{j}\) have no direct relationships but are related by \(E_{coh}\) as an indirect relationship. The following Equations (3)-(6) explain Equation (2), respectively:  
\[rScore\big{(}e_{i},e_{j}\big{)}=n\big{(}e_{i},e_{j},\ R\big{)} \tag{3}\]  
\[n\big{(}e_{i},e_{j},\ R\big{)}= \sum\limits_{\begin{subarray}{c}c\in A\subseteq tS\\[exist\big{(}c,ACatg\big{(}e_{i}\big{)}\big{)}=\left\{\begin{array}{c}1,\ c\ \in\ ACatg\big{(}e_{j}\big{)}\\ 0,\ otherwise.\end{array}\right. \tag{5}\]  
\[exist\big{(}e_{i},e_{j},E_{coh}\big{)}\big{)}=\left\{\begin{array}{c}1,\ (e_{i}e_{j})\ \in\ E_{coh}\\ 0,\ \ \ otherwise.\end{array}\right. \tag{6}\]  
Moreover, the \(\text{LScore}(e_{i})\) gives the entity score computed by EL4 DT in the candidate selection process, which mainly calculates the three factors (assignment of components weights, score of contextual similarity, and number of terms in the entity) when considering the different surface forms and the three types of entity, such as the non-sure, sure, and strong entities. \(ACatg(e_{i})\) provides the entity category of the entity \(e_{i}\), which includes all entities of the same DBpedia category. \(SkosR(e_{i})\) provides the Skos relations (\(<\)skos:broader\(>\) and \(<\)skos:related\(>\) predicates) of the entity \(e_{i}\), which are extracted from DBpedia.