Connection between the two Classifiers

As discussed in the two previous sections, the two approaches are equivalent to the use of discriminative training for single Gaussian densities with some additional restrictions. This implies that the main difference between the classifiers is the criterion that is used to choose the class boundaries:

Gaussian densities:

criterion: maximum likelihood (1); decision boundary: linear (pooled covariance matrices) or quadratic (class-specific covariance matrices)

log-linear model:

criterion: maximum mutual information (maximum likelihood of the posterior) (2); decision boundary: linear (first-order feature functions) or quadratic (second-order feature functions)

weighted dissimilarity measures:

criterion: intra-class distances versus inter-class distances (4); decision boundary: quadratic (one prototype per class) or piecewise quadratic (multiple prototypes per class)