The algorithm used by the Maximum Likelihood Classification tool is based on two principles:
The cells in each class sample in the multidimensional space are normally distributed.
Bayes' theorem of decision making.
The Maximum Likelihood Classification tool considers both the variances and covariances of the class signatures when assigning each cell to one of the classes represented in the signature file. With the assumption that the distribution of a class sample is normal, a class can be characterized by the mean vector and the covariance matrix. Given these two characteristics for each cell value, the statistical probability is computed for each class to determine the membership of the cells to the class. When the default EQUAL a priori option is specified, each cell is classified to the class to which it has the highest probability of being a member.