One of the simplest classifier is the linear discriminant function as follows:
This function is a linear function of the components of X. A
complete specification of this linear discriminant function is
achieved by specifying the values of the weights or parameters of the
function family. The training process is one of adjusting the
coefficients ( 
, 
, 
, 
, 
) so that the
decision surface implements an acceptable separation of the two
classes of patterns in the training set. The decision surfaces of any
pattern classifier can be implicitly defined by a set of linear
discriminant functions containing R members. Let 
, 
,
, 
be scalar and single-valued functions of the
pattern X. These functions are called discriminant functions.
