- Volume 28 Issue 6
DOI QR Code
Multidimensional Scaling Using the Pseudo-Points Based on Partition Method
분할법에 의한 가상점을 활용한 다차원척도법
Shin, Sang Min;Kim, Eun-Seong;Choi, Yong-Seok
- Received : 2015.10.12
- Accepted : 2015.12.14
- Published : 2015.12.31
Multidimensional scaling (MDS) is a graphical technique of multivariate analysis to display dissimilarities among individuals into low-dimensional space. We often have two kinds of MDS which are metric MDS and non-metric MDS. Metric MDS can be applied to quantitative data; however, we need additional information about variables because it only shows relationships among individuals. Gower (1992) proposed a method that can represent variable information using trajectories of the pseudo-points for quantitative variables on the metric MDS space. We will call his method a 'replacement method'. However, the trajectory can not be represented even though metric MDS can be applied to binary data when we apply his method to binary data. Therefore, we propose a method to represent information of binary variables using pseudo-points called a 'partition method'. The proposed method partitions pseudo-points, accounting both the rate of zeroes and ones. Our metric MDS using the proposed partition method can show the relationship between individuals and variables for binary data.
multidimensional scaling;pseudo-points;replacement method;partition method
- Choi, Y. S. (2014). Walk in Multidimensional Scaling, Free Academy, Kyungki.
- Choi, Y. S. and Shin, S. M. (2013). Understanding of Biplot Analysis using R, Free Academy, Kyungki.
- Cox, T. F. and Cox, M. A. A. (1994). Multidimensional Scaling, Chapmann and Hall, London.
- Everitt, B. S. and Dunn, G. (1991). Applied Multivariate Data Analysis, Edward Arnold, London.
- Gower, J. C. (1968). Adding a point to vector diagrams in multivariate analysis, Biometrika, 55, 582-585. https://doi.org/10.1093/biomet/55.3.582
- Gower, J. C. (1992). Generalized biplots, Biometrika, 79, 475-493. https://doi.org/10.1093/biomet/79.3.475
- Gower, J. C. and Hand, D. J. (1996). Biplots, Chapman & Hall, London.
- Huh, M. H. (1994). SAS Optimal Scaling, Free Academy, Seoul.
- Kruskal, J. B. and Wish, M. (1978). Multidimensional Scaling, University Paper Series on Quantitative Applications in the Social Sciences, 07-011, Sage Publications, Beverly Hills and London.
- Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis, Academic Press, New York.
- Torgerson, W. S. (1958). Theory and Methods of Scaling, Wiley, New York.