y

p

the dependent variables and the independent variables are

vely parameterised. From such a model, it is very easy to

e how an independent variable correlates with the dependent

When the format is slightly changed, the other analytic

ant analysis algorithms have been developed. However, the

orward proportional relationship between the dependent variable

pendent variables is no longer valid. Instead, the relationship

the dependent variable and the independent variables becomes

ly analytic.

e quadratic discriminant analysis algorithm

en discussed above that two classes are assigned an identical

ce matrix in LDA, i.e., ΣଵൌΣଶൌΣ. This is only valid when the

e between two covariance matrices (Σଵ and Σଶ) is insignificant.

his difference becomes significant, the use of an identical

ce matrix for two classes may no longer be a good approach. To

h the difficulty of significantly different covariance matrices

wo classes, the quadratic discriminant analysis algorithm (QDA)

ernative [Tharwat, 2016]. The algorithm is also called the

ed discriminant analysis algorithm (GDA) [Cover, 1965]. It

LDA in the format shown below, where the matrix W and the

are model parameters

ݕൌܠ^௧܅ܠ൅઺^௧ܠ൅ܿ

(3.18)

QDA model, two covariance matrices are allowed to be different,

Σଶ. The R function for constructing a QDA model is qda.

of the use of different covariance matrices for two classes, the

ation boundary between two classes will not be a straight line

gure 3.6 shows a data set with two classes. The cross class has a

riance than the triangle class.

e 3.7(a) is the use of the R package klaR to show the LDA

ation boundary for the data shown in Figure 3.6. It can be seen