# The Role of Maintenance Operator in Industrial Manufacturing Systems: Research Topics and Trends
## 2 Methods
### Topic Modelling Approach  
The Topic Modelling Approach is used to identify clusters and extract features from high-dimensional text datasets, and to discover the main themes that characterize a large and otherwise unstructured collection of documents [13; 14]. The goal of topic modelling is to automatically discover the topics from a collection of documents.  
A Latent Dirichlet Allocation (LDA) is an effective approach for topic modelling, which discovers underlying topics in a collection of documents and infers word probabilities in topics [15].  
The intuition behind LDA is that documents exhibit multiple topics. LDA model is based on a probabilistic model of a corpus. Each document can be thought of as a composition, or a distribution, of latent topics, where each topic has an underlying distribution of the words in the dictionary. Each document has an underlying topic distribution, and these topic distributions are unique to each document. Each word in the document is then assumed to be drawn from one of the K topic distributions. The LDA algorithm assumes this process when determining the D document-topic distributions and the topic-word distributions [13]. The main outputs of the LDA model are the document-topic distribution and the topic-word distribution.  
Formally, considering the same notations suggested in Reference [13], the generative process for LDA corresponds to the following joint distribution (1) of the hidden and observed variables:  
\[p(\beta_{\text{1:K}},\,\theta_{\text{1:D}},\,z_{\text{1:D}},\,w_{\text{1:D}}) \tag{1}\]  
where:  
* \(\beta_{\text{1:K}}\) are the topics, where each \(\beta_{k}\) is a distribution over the vocabulary;
* \(\theta_{d}\) are the topic proportions for the \(d\)th document where \(\theta_{d,k}\) is the topic proportion for topic k in document d;
* \(z_{d}\) are the topic assignments for the \(d\)th document, where \(z_{d,n}\) is the topic assignment for the \(n\)th word in document \(d\);
* \(w_{d}\) are the observed words for document \(d\), where \(w_{d,n}\) is the \(n\)th word in document \(d\), which is an element from the fixed vocabulary.  
One of the distinctive features of LDA is that the set of emerged topics is certainly shared by all the documents of a collection, but each document presents those topics with different proportions.  
This feature first allows us to know the topics mixture showed in each article and then to allocate each paper in a collection of scientific articles exhibiting the same topic in the highest proportion.  
The principal advantages of generative models such as LDA include their modularity and their extensibility. For the aim of this study, LDA was applied using the Text Analytics Toolbox of Matlab(r) (R2017b).  
The phases for the Topic Modelling approach were:  
* The text mining phase that involved the extraction and collection of titles, keywords, and abstracts of selected papers in the previous step.
* The result of text mining was a document matrix, whose dimensions are the selected papers and the extracted text. Document matrix was uploaded in Matlab(r) for subsequent analysis steps: preparation of text; creation of a \"Bag of Words\"; application of LDA through the _fitLDA_ function.
* The application of LDA allowed us to discover and identify the topics in the selected papers and depict them by word clouds.
* Topic Prediction Scores for each document were quantified achieving the percentage of topic distributions in each paper and a 2D structure can be achieved (Papers and Topic Prediction Scores)
* Topic distributions were then aggregated to perform Topic content analysis and define the research trends on the role of the operator in industrial maintenance.