## 2 Literature Review  
### Latent Semantic Analysis (LSA)  
LSA is a method used to extract and perform contextual usage representation of the meaning of words using statistical computation, which is applied to a large collection of texts [9]. In LSA algorithms, there are mathematical matrices that describe the frequency with which terms occur in the document collection--or the so-called term-document matrix. In the term-document matrix, the rows of the matrix represent a collection of words in the document, and the columns represent the number of documents [10]. LSA is able to understand the lexical features of a document by using the concept of Singular Value Decomposition (SVD); SVD can reveal the document's context, not the synonym of words in the document. SVD transforms the original data by reordering the dimensions and sorting them [11]. Vector space models have been shown to be highly-effective at detecting meaningful semantic entities in text [12] as more generally have methods based on complexity analysis [13]. A term-document matrix built by LSA can be used for a probabilistic model to observe the similarity of the documents. Therefore, the LSA has often been used to build a knowledge-based system over the parallel corpus to find occurrences of plagiarism.  
The matrix of word associations or term document matrix can be used to create a probabilistic model for rating the likelihood of an observed term, but the dimensionality of the matrix can become so high that rapid searches using the entire matrix can become excessively time-consuming and computationally-demanding. SVD mitigates this problem by reducing the dimensionality of the term document matrix, effectively compressing all the relevant information into a far more compact and widely form. Within this smaller framework, semantically-meaningful clusters of association become clearer (in machine learning terms, the signal to noise ratio is increased) [14].  
The first step in running the LSA method is to represent the text as a matrix with words as rows and document (or other contexts) as columns. The matrix formed is called the term-document matrix [15]. Documents in the term-document matrix can be defined independently. They can be selected using a fixed number of words, such as 5, 10, or 20, or defined as a non-fixed-sized document bounded only by a sentence or ended with a full-stop [16]. Each cell contains the number of occurrences of a word on a row from the particular document on the corresponding column. An overview of the term-document matrix is shown in Figure 1.  
Figure 1: Block diagram of the proposed automated cross-language plagiarism detection system.  
The next step of LSA is performing SVD of the matrix for factor analysis. SVD decomposes the matrix into three matrices. One of these matrices is a diagonal matrix containing the scale value that multiplies the row matrix (first matrix) and column matrix (third matrix) back into the initial matrix whose dimensions are equal to the dimensions of the matrix. However, the diagonal matrix has values which provide interesting significance compared to the original matrix [9].  
The original method of LSA compares documents stored in the columns of the matrix using Spearman's rho correlation coefficient (\(\varrho\)), with a range of \(-1\leq\varrho\leq 1\). The correlation between two words in the documents can be checked to see whether they are relevant (positive correlation) or irrelevant (negative correlation). A detailed explanation of the original LSA is included in [10].