Spatial discrimination and classification maps

A method of constructing maps through spatial discrimination is given. The discrimination depends basically on the assumption of local spatial continuity, and a factorized covariance matrix. Given an autocovariance function, this formulation in particular, leads to a deeper insight into the pioneering work of Switzer (1980). Certain windows for the maps are examined, and choice of window size is discussed in relation to the classification error when the variables are dependent versus independent. When a training data is given, we give a method of estimating the parameters in the model. Some numerical examples are also given.