Review of relevant classification methodologies

Discriminant analysis techniques (also called classification techniques) are concerned with classifying objects into one of two or more classes. Discriminant techniques are considered to be learning procedures. Given, a set of objects whose class identity is known, a model learns from the variables which have been measured for each of the objects, a procedure which can be used to assign a new object, whose class identity is unknown, into one of the predefined classes. Such a procedure is performed using a well-defined discriminatory rule. 

In many instances one will be given a set of training data consisting of nr 

Each object Xj consists of measurements made on p variables and can be 

A discriminant model which is assessed using the same training data which was used to estimate the parameters in the model will usually reflect overly optimistic results. It can be appropriate to use an independent test set for assessing the validity of the model. Let X define the testing data which contains n objects with nj objects from class r such that n = n and y = (yj, , y n ) denotes the vector of true class labels of the testing data. 

The discriminatory rule that we consider is based on Bayes decision rule [1]. An object x is assigned to the class r, which maximizes the posterior probability 

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