Discriminant analysis

Let's suppose we consider a multi-class classification problem where the conditional probability for a sample xi ∈ ℜm to belong to the yj class can be modeled as a multivariate Gaussian distribution (X is assumed to be made up of independent and identically distributed (i.i.d) variables with extremely low collinearities):

In this case, the class j is fully determined by the mean vector μj and the covariance matrix Σj. If we apply the Bayes' theorem, we can obtain the posterior probability p(yj|xi):

Considering the discussion ...

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