## 3 Methodology  
For our research we conducted topic modeling, using the R language in order to collect and analyze data from the Europeana Search API. R is a programming language and environment for statistical computing and data visualization. It is a GNU project similar to the S language and environment that was developed by [PERSON] and colleagues at Bell Laboratories [27]. R has excellent facilities to interact with Europeana APIs such as the EuropeanaR package [28]. Our research was conducted in three stages. During the first stage, we utilized the Search API to find paintings from the 14 th, 15 th, 16 th and 17 th centuries. In the second stage,we proceeded to perform data mining, using the R language, and in the third and last stage, we concluded with learning a topic model from the collection. Topic modelling is a machine learning technique that discovers automatically latent semantic patterns (i.e., subjects made of a set of words) in a collection of documents. This is known as unsupervised machine learning because no categories are predefined or observed (topics). Topic models hold enormous potential as a method for extracting meaningful insights from the text databases that are currently accessible to social scientists [29]. For our study we used the Latent Dirichlet Allocation (LDA), one of the most common algorithms for topic modelling, which has been widely utilized for text mining in numerous industries ([PERSON], [PERSON], [PERSON], [PERSON], & [PERSON], [PERSON] Bayesian LDA for mixed-membership clustering analysis: the Rlda package). It is a three-level hierarchical Bayesian model, a generative probabilistic model for discrete data collections, such as text corpora [30]. In this model, each item of a collection is modeled as a finite mixture across an underlying set of topics [30]. In turn, each topic is modeled as an infinite mixture over a collection of topic probabilities. The topic probabilities give an explicit representation of a document in the context of text modeling [30]. LDA is implemented by an easy application of [PERSON]'s representation theorem because it is based on a simple exchangeability assumption for the words and themes within a document [30]. According to [PERSON]'s theorem, the probability of a sequence of words and topics must have the following form:  
\[p(w,z)=\int p(\theta)\left(\prod_{n=1}^{N}p(z_{n}|\theta)p(w_{n}|z_{n})\right)d\theta\]  
LDA was used for our research as a probabilistic method that discovers a set of underlying topics in an automatic way, represented by word distributions, in texts. Thus, texts are viewed as a distribution across topics. In an LDA model, words can be represented as a vector of topic contributions. Latent Semantic Analysis (LSA), a fully automated method that extracts meaning representations in the form of latent concepts, was also considered. In a semantic space derived from the LSA, words are represented as vectors. The dimensions of this space are concepts that are latent. Vector algebra is used to compute the similarity of individual words and texts [29]. LDA has a conceptual benefit over LSA in that it directly expresses many meanings of a term, whereas LSA does not [31]. Another model under consideration was word vectors that vectorize each word, but we preferred to focus on topic modeling. European's Search API allows the user to search for key-words, using either simple or more advanced queries. The user can choose to include or filter out results, or to choose results from a certain language. For our data gathering, we used R version 4.1.3 and the library EuropeanR, a package that was created specifically for this project and aims to provide tools to access European's Linked Open Data [28]. With this package, we have the ability to interact with all European's APIs. The interaction with the package is taking place using HITR in the backend to harvest and collect data [32].