The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Multidimensional Scaling of Asymmetric Distance Matrices

  • Received : 2012.02.29
  • Accepted : 2012.06.13
  • Published : 2012.08.31
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Abstract

In most cases of multidimensional scaling(MDS), the distances or dissimilarities among units are assumed to be symmetric. Thus, it is not an easy task to deal with asymmetric distances. Asymmetric MDS developed so far face difficulties in the interpretation of results. This study proposes a much simpler asymmetric MDS, that utilizes the notion of "altitude". The analogy arises in mountaineering: It is easier (more difficult) to move from the higher (lower) point to the lower (higher). The idea is formulated as a quantification problem, in which the disparity of distances is maximally related to the altitude difference. The proposed method is demonstrated in three examples, in which the altitudes are visualized by rainbow colors to ease the interpretability of users.

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References

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  1. Visualizations for Matched Pairs Models Using Modified Correspondence Analysis vol.21, pp.4, 2014, https://doi.org/10.5351/CSAM.2014.21.4.275
  2. Visualizations of Asymmetric Multidimensional Scaling vol.27, pp.4, 2014, https://doi.org/10.5351/KJAS.2014.27.4.619