<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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: <xref ref-type="bibr" rid="j_foli-2018-0026_ref_007_w2aab3b7c11b1b6b1ab1ab7Aa">R.A. Fisher (1940)</xref>, <xref ref-type="bibr" rid="j_foli-2018-0026_ref_012_w2aab3b7c11b1b6b1ab1ac12Aa">M.J. Greenacre (1984)</xref>, <xref ref-type="bibr" rid="j_foli-2018-0026_ref_001_w2aab3b7c11b1b6b1ab1ab1Aa">E.B. Anderson (1991)</xref>, and <xref ref-type="bibr" rid="j_foli-2018-0026_ref_016_w2aab3b7c11b1b6b1ab1ac16Aa">J.D. Jobson (1992)</xref>. 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 <italic>R</italic> statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.</p></abstract>

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.

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

Faculty of Finance and Insurance, Department of Economic and Financial Analysis

Folia Oeconomica Stetinensia

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible...

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

Published Online: Dec 31, 2018

Page range: 178 - 189

Received: Nov 06, 2017

Accepted: Nov 05, 2018

DOI: https://doi.org/10.2478/foli-2018-0026

Keywords
correspondence analysis, singular value decomposition, contingency table, R software

© 2018 Justyna Brzezińska, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 31, 2018

Page range: 178 - 189

Received: Nov 06, 2017

Accepted: Nov 05, 2018

DOI: https://doi.org/10.2478/foli-2018-0026

Keywordscorrespondence analysis, singular value decomposition, contingency table, R software

© 2018 Justyna Brzezińska, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
correspondence analysis, singular value decomposition, contingency table, R software