3.2 Mapping

3.2.1 Metric multidimensional scaling

The attempt to find a configuration where the metric nature of the transformation is conserved (see section 2.3.3 "Metrics" on page 16) is called metric multidimensional scaling [Cox et al., 1994] or linear dimensionality reduction. Various methods to complete this task have existed for a long time . The most famous technique is principal components (coordinates) analysis (Karhunen-Loève expansion) [Jolliffe, 1986][Auray et al., 1990a]. Other techniques include least squares scaling and Critchley's method [Cox et al., 1994].

It is obvious that conserving the metric nature of the distances is important. However, since it is implausible that a linear relationship can be found during the transformation, the above mentioned methods do not perform well on high-dimensional dimensionality reduction. Thus, alternatives to metric multidimensional scaling have to be investigated.

Cyberspace geography visualization - 15 October 1995

Luc Girardin, The Graduate Institute of International Studies