Which values are derived from the training data in discriminant analysis to determine class membership?

• A. Probabilities
• B. Means
• C. Covariances
• D. Distances

Answer: (A)

Discriminant analysis assigns a class by comparing posterior probabilities P(class|x) for the observed features x. From the training data you estimate the prior probabilities of each class and the class-conditional densities p(x|class) (often modeled as Gaussians with class-specific means and covariances). These are combined using Bayes rule to produce P(class|x) for each class. The observation is then assigned to the class with the highest posterior probability. So, the values used to determine membership are these posterior probabilities derived from the training data. Means and covariances are the parameters used to define the densities, and distances aren’t the standard basis for assignment in discriminant analysis.