Gaussian Discriminant Analysis

GDA, is a method for data classification commonly used when data can be approximated with a Normal distribution. As first step, you will need a training set, i.e. a bunch of data yet classified. These data are used to train your classifier, and obtain a discriminant function that will tell you to which class a data has higher probability to belong.

When you have your training set you need to compute the mean μμ and the standard deviation σ2σ2. These two variables, as you know, allow you to describe a Normal distribution.

Once you have computed the Normal distribution for each class, to classify a data you will need to compute, for each one, the probability that that data belongs to it. The class with the highest probability will be chosen as the affinity class.

More information about Discriminant Functions for the Normal Density can be found in textbook as Pattern Classification DUDA, HART, SOTRK or Pattern Recognition and Machine Learning BISHOP.

A tutorial to GDA can also be found here Part1 and Part2

Assume p(x|y) is multivariate normal distribution.