Singular Value Decomposition Approaches in A Correspondence Analysis with The Use of R

The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible due to the decomposition of the basic matrix with the use of Singular Value Decomposition (SVD). There are three matrices used in the process of decomposition: right singular vectors, left singular vectors, and a singular value diagonal matrix. The aim of this paper is to compare four different approaches and algorithms of SVD methods used in a correspondence analysis. In the literature, four approaches are known to singular value decomposition, defined by: R.A. Fisher (1940), M.J. Greenacre (1984), E.B. Anderson (1991), and J.D. Jobson (1992). Those computational procedures will be presented and compared in this paper. Also, methods of determining the coordinates of the category column and line matrix, as well as the values of inertia will be defined for these approaches. A key problem is to compare the well-known approaches, since in the literature only one approach ‒ proposed by Greenacre ‒ is used for singular value decomposition. The reason of the superiority of this algorithm over the others may be the simplicity and ease of the mathematical calculations. Greenacre’s algorithm is also used in R statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.