Choosing the best 1d projection

(Note: videos below are given in both quicktime and mpeg formats; however, the quicktime videos tend to be higher quality and are therefore recommended. If you do not have quicktime installed, you can download the free player (Mac/Windows) from Apple.)

The animation below illustrates how 2d synthetic data (two classes) is projected onto different 1d subspaces. Note that for some of the 1d projections, the two classes will be easy to discriminate in the 1d subspace, while for other projections, there will be significant overlap in the classes, and, hence, substantial classification error. It is the job of the Fisher linear discriminant to find that 1d projection that will yield the smallest amount of overlap between two classes.

Different 1d projections of 2d, two-class data
(400 x 400)

(high-quality, quicktime, 3.1 Mb)

(lower-quality, mpeg, 1.8 Mb)

Last updated October 21, 2003 by Michael C. Nechyba