chapter  10
20 Pages

Miscellaneous Topics

In this last chapter we discuss some particular relevant topics in other areas not covered in the previous chapters.

Visualization of high-dimensional data is an interesting, useful yet challenging task. The approach of dimensionality reduction strives to find a lower dimensional space that captures all or most of the information that exisits in the higher dimensional space. Multidimensional scaling is a process whereby we seek an essentially information-preserving subspace of the original space. That is, we look for a lower dimensional space in which the problem becomes simpler or more clear, and still retains its essence. This discipline originated as a way to visualize higher-dimensional data, “projected” into lower dimensions, typically two, in such a way as the distances between all points was mostly preserved. The process has evolved into general dimensionality reduction methodology as well as being able to discover embedded, lower-dimensional nonlinear structures in which most of the data lies. Here we explore the general problem of finding a lower-dimensional space in which the data can be represented and the between-point distances is preserved as best as possible. For a more complete treatment on multidimensional scaling, refer to Cox and Cox (2000).