An example

This example illustrate the automatic recognition of hand-written numbers from 0 to 9. The figure below shows the hand-written numbers by 28 students (each number is repeated 8 times). There are in total $28\times8\times 10=2240$ images each containing $16\times16=256$ pixels, which are treated as 256 features for the description of the pattern.

To reduce the dimensionality of the feature space, a linear transform ${\bf y}={\bf A}^T{\bf x}$ is introduced so that the separability $J({\bf A}) = tr\;[S^{(y)}_{B/T} ]$ is maximized in the transform domain.