mised or the density bimodality is maximised.

ose the projection direction (w) has been optimised as well as the

y of the projection density has been maximised. The next issue is

assify data points or discriminate between two classes of data points

An example is shown in Figure 3.2, where the estimated projection

shown as the dotted straight line is supposed to have been optimised.

at the distribution of the data points separated by the projection

it is for sure that the projection direction is perhaps an optimal one.

s optimised projection direction, all data points of two classes have

pped to the projection direction resulting in projections (ݕො). A

f the projections is constructed. The top-left inset of Figure 3.2

s density. Its bimodality looks very good.

e illustration of examining whether data points are mapped to the right locations

ction direction using LDA. The triangles and the crosses stand for two classes

nts. Three validation points are denoted by three letters (A, B and C). The dotted

for the optimised projection direction as the classification boundary. The inset

m-left corner stands for the density estimated for the projections based on the

direction using the histogram approach. The inset at the top-left panel shows

validation points are mapped in their correct positions in the density function.

t the bottom-right panel shows the posterior probability curves generated using

ule, where three validation points are also mapped. The solid line is the posterior

curve for the class of the triangles. The dotted line is the posterior probability

he class of the crosses. The Bayes rule will be introduced in this chapter.

ow what the discrimination power is between two classes of data

ree validation points labelled by A, B, and C were inserted into