# Integrating Text Classification into Topic Discovery Using Semantic Embedding Models
## 3 Proposed Approach
### Topic Discovery  
Topic discovery breaks down a large corpus of text into a small set of interpretable topics, allowing a domain expert to explore and analyze a corpus efficiently [47]. In the literature, algorithms for topic discovery are latent Dirichlet analysis (LDA), latent semantic analysis (LSA), and probabilistic latent semantic analysis (PLSA). However, some authors have incorporated additional procedures into their approaches, such as classifying text before topic discovery. On the other hand, topic discovery has been an essential part of different tasks of the NLP, for example, sentiment analysis and decision-making. Latent Dirichlet analysis is an algorithm used for topic discovery. The model is based on the hypothesis that each text contains words or terms from different topics. This model needs to know a priori the text and the number of topics to be found in the text. This model is maintained under the premise that the topics and text are treated through Dirichlet distributions [48]. Figure 2 presents a graphical representation of the LDA model. Where:  
\(M\) denotes the number of documents. \(N\) denotes the number of words in a given document (document \(i\) has \(N_{i}\) words). \(\alpha\) denotes the parameter of the Dirichlet prior to the per-document topic distributions. \(\beta\) denotes the parameter of the Dirichlet prior to the per-topic word distribution. \(\theta_{i}\) denotes the topic distribution for document \(i\). \(\varphi_{k}\) denotes the word distribution for topic \(k\). \(z_{ij}\) denotes the \(j\)-\(th\) word in document \(i\). \(w_{ij}\) denotes the specific word. On the other hand, latent semantic analysis (LSA) is another algorithm used for topic discovery. LSA is a mathematical dimensionality reduction procedure denoted as the singular value decomposition (SVD). LSA (or LSI) is an automatic index analysis that projects terms and text in a space of reduced dimensions. The reduction of attributes or dimensions of the text leads to the recovery of the semantics of the original text. The LSA  
Figure 2: Graphical representation of the LDA model [49]. dimensionality reduction process captures important terms or topics [50]. Figure 3 shows the matrix generated by the LSA model. A singular value decomposition (SVD) applies to the resulting matrix through a series of elementary linear operations, such as adding and multiplying rows and columns. Therefore, the matrices resulting from applying SVD are as follows:  
* Orthogonal matrix (U): obtained by linearly processing the original matrix's number of columns (orthogonal). * Transposed matrix (V): obtained by swapping the rows with the columns, providing an orthogonal arrangement of the elements of the row. * Diagonal matrix (E): obtained by linearly processing the original matrix's number of rows, columns, and dimensions (A); the diagonal matrix represents the singular value of (A), and in this, all the elements that do not belong to the diagonal are null or equal to zero. Finally, probabilistic latent semantic analysis (PLSA) continues the LSA. In PLSA, words are attributed to latent topics or concepts based on the weighted frequency of terms. It interprets frequencies in terms of probability. PLSA is a descriptive statistical technique. The probability that a term forms part of the set of terms belonging to a topic or concept depends on the different parameters obtained. These parameters are obtained by counting the given frequencies in a matrix based on a multinomial probability calculation. The objective of PLSA is to estimate the multinomial probability distribution of some words in a topic. Figure 4 shows the PLSA model graphically. In Figure 4, \(PLSA\) models the joint probability of seeing a word \(w\) and a document (text) \(d\) as a mixture of conditionally independent multinomial distributions. Where:  
\(M\) denotes the number of texts. \(N\) denotes the number of words in a given text. \(d\) indicates a text. \(z\) denotes the latent or hidden variable (topic). \(w\) denotes a specific word.