External Analysis of Asymmetric Multidimensional Scaling Based on Singular Value Decomposition
An asymmetric similarity matrix among objects, for example, a brand switching matrix of consumers, can be analyzed by asymmetric multidimensional scaling. Suppose that n brands exist, and that m new brands are introduced. While the brand switching from existing to new brands can be observed, the brand switching from new to existing brands nor that among new brands cannot be observed soon after the introduction of the new brands. The present study analyzed the n ×n similarity matrix by the asymmetric multidimensional scaling based on singular value decomposition. The analysis gives outward and inward tendencies of existing brands. Using the obtained outward tendency of n existing brands, the inward tendency of m new brands is derived. An application to the brand switching data among margarine brands is presented.
The authors would like to express their gratitude to the anonymous referee for her/his constructive review on an earlier version of this paper. They also wish to express their appreciation to Jim Hathaway for his thoughtful help concerning English.
- Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling: theory and applications (2nd edn.). New York: Springer.Google Scholar
- Okada, A. (2011). Analysis of social affinity for foreigners by spectral decomposition: Asymmetric multidimensional scaling of EASS2008 data. JGSS Research Series, 8, 119–128. (in Japanese).Google Scholar
- Okada, A. (2012). Analysis of car switching data by asymmetric multidimensional scaling based on singular value decomposition. In W. Gaul, A. Geyer-Schultz, , L. Schmidt-Thieme, J. Kunze (Eds.) Challenges at the interface of data analysis, computer science, and optimization (pp. 143–150). Heidelberg: Springer.Google Scholar