he most basic question, which is how to find the optimal model

rs w for constructing a LDA model for a data set. The purpose is

r a bimodal density of the projections and ultimately an optimal

del with a good discrimination power between two classes of data

e., peptides.

(a) (b)

n illustration of how the weights (model parameters) determine the bimodality

ion density. The triangles and the crosses represent two classes of this data set.

line in each panel stands for the classification boundary corresponding to the

direction w. The inset plot in each panel stands for the density of the projections

projection direction w. (a) A good projection direction leads to a bimodal density

ns. (b) A poor projection direction leads to a unimodal density of projections.

fore, to estimate model parameters such as ݓଵ and ݓଶ, the

ty of the projection density given a vector of model parameters w

maximised. Unless the bimodality of the projection density has

ximised, a LDA model won’t be considered as a useful classifier.

nce, the classifier shown in Figure 3.1(b) will not be considered

er candidate and will not be selected for use because the classifier

ver a greater error when it is used to classify data points, such as

On the other hand, the classifier shown in Figure 3.1(a) has a

crimination power due to an obvious bimodality of the projection

t is believed that this classifier will separate two classes of data

uch as peptides, with a good discrimination power.

basic principle of LDA is thus to discover the best projection

(w) among all possible projection direction candidates. The