## 3 Results for the Research Questions
### RQ4: What Are the Methods That Have Been Used for Expert Finding Systems?
#### 3.4.1 Generative Probabilistic Models  
These models estimate the relationships between query topics and people as the probability of generating a particular topic by a given candidate. This type of model is the first edition of the Text Retrieval Conference (TREC) Enterprise track, and it considered a popular class for expertise retrieval. This is due to TREC's good empirical performance and prospective for combining different extensions in a transparent and theoretically sound manner. The ranking process of the candidate experts are based on the probability of person e being an expert on query q (_P(e)q_). Commonly, there are two methods for estimating this likelihood, and these define the two core types of generative models. The first type is the candidate generation model, which can be generated directly according to the query topic q and the probability model finding the candidate expert e. The second type of generative models is a topic generation model, based on Bayes' Theorem, and it can be represented as follows:  
\[\mathrm{p}(\mathrm{e}\div\mathrm{q})=(\mathrm{rank})\mathrm{p}(\mathrm{q}\div \mathrm{e})\times\mathrm{p}(\mathrm{e}) \tag{1}\]where P(e) is the likelihood of a candidate and \(P\)(q) is the likelihood of a query [1]. Since \(P\)(\(q\)) is a constant (for a given query), it can be disregarded for the purpose of ranking. Thus, the likelihood of a candidate expert e being an expert given query q is proportional to the probability of the query given the candidate (\(P\)(\(q\))), weighted by the a priori belief that candidate e is an expert (\(P\)(\(e\))) [108].  
Generative probabilistic models contain different methods such as a document-based model. Document-based methods (also called query-dependent methods) first find the related documents to the query and then rank candidates associated with these documents based on an integration of the relevance score of documents and the degree of a person's association with that documents. Therefore, individuals are represented based on a weighted set of documents. Generative probabilistic models have been used by several researchers, as shown in Table 8. Reference [40] used content-based methods and explored different techniques for computing similarity between two researcher profiles, namely  
1. Okapi BM25 (OKAPI), where a vector of terms associated with researcher's content was used to represent the researcher profile. In order to obtain the similarity between two profiles, this technique considered one profile as the query and the second profile as a document.
2. KL Divergence (KLD): In this technique, a probability distribution is used to represent a researcher profile. For example, a multinomial distribution can be used to model the term counts in a researcher's associated documents and to count the similarity between two probability distributions. Kullback-Leibler divergence is used.
3. Probabilistic Modelling (PM): Latent Dirichlet Allocation is a widely used tool for topic modelling in unsupervised clustering of data and exploratory analysis. For example, when researchers have a desire to work on multiple related areas, sometimes it is more suitable to model their profiles as topic mixtures rather than a single multinomial distribution.
4. Trace-Based Similarity (REL): used density matrices to represent vector subspaces for modelling concepts. Additionally, reference [27] used content-based similarity to develop a model for finding similar experts in a university.  
Also, reference [109] used generative probabilistic and similarity models to propose Beneficial Collaborator Recommendation (BCR). Also, reference [77] used generative language models for group finding task from heterogeneous document repository.