Two schemes for computing thresholds in linear classifiers

Linear classifiers are very important because of their simplicity and classification speed. When dealing with normally distributed classes, one of the most well-known linear classifier techniques is Fisher´s approach. We theoretically analyze some properties that relate Fisher´s classifier and the optimal quadratic classifier, when the latter is derived utilizing a particular covariance matrix for the classes. We also discuss an efficient approach, which is used to select the threshold after a linear transformation onto the one-dimensional space is performed. Our empirical results on normally distributed classes show that our approach lead to smaller classification error than the traditional Fisher´s approach.