Low-dimensional Representation

Ordination is a generic name for methods for providing a low-dimensionaL view of points in multi-dimensional space, such that “similar” objects are near each other and dissimilar objects are separated. The plot(s) from an ordination in 2 or 3 dimensions may provide useful visual clues on clusters in the data and on outliers. If data can be separated into known classes that should be reflected in any ordination, then the scores from classification using lda() may be a good basis for an ordination. Plots in 2 or perhaps 3 dimensions may then reveal additional classes and/or identify points that may be misclassified and/or are in some sense outliers. It may indicate whether the classes that formed the basis for the ordination seem real and/or the effectiveness of the discrimination method in choosing the boundaries between classes. Here, the discussion will turn to multi-dimensional scaling (MDS) methods where distances are given, or that start by calculating distances between points, then using the distances as the starting point for an ordination. Similarities can be transformed into distances, though often with some arbitrainess in the way that this is done. Examples are: