More info about Quadratic Discriminant Analysis

Interesting about Quadratic Discriminant Analysis

Quadratic discriminant analysis (QDA) is closely related to linear discriminant analysis (LDA), where it is assumed that the measurements from each class are normally distributed. Unlike LDA however, in QDA there is no assumption that the covariance of each of the classes is identical. When the normality assumption is true, the best possible test for the hypothesis that a given measurement is from a given class is the likelihood ratio test. Suppose there are only two groups, (so y∈{0,1}{\displaystyle y\in \{0,1\}}), and the means of each class are defined to be μy=0,μy=1{\displaystyle \mu _{y=0},\mu _{y=1}} and the covariances are defined as Σy=0,Σy=1{\displaystyle \Sigma _{y=0},\Sigma _{y=1}}. Then the likelihood ratio will be given by