We consider a unified description of classification rules for nearly singular covariance matrices. When the covariance matrices of the groups or the pooled covariance matrix become nearly singular, bayesian classification rules become seriously unstable. Several procedures have been proposed to...

A lot of alternatives and constraints have been proposed in order to improve the Fisher criterion. But most of them are not linked to the error rate, the primary interest in many applications of classification. By introducing an upper bound for the error rate a criterion is developed which can...

This paper illustrates the Support Vector Method for the classification problem with two and more classes. In particular, the multi-class classification Support Vector Method of Weston and Watkins (1998) is correctly formulated as a quadratic optimization problem. Then, the method is applied to...

When comparing methods for classification, often the rating relies on their prediction accuracy alone. One reason for this is that this is the aspect that can be most easily measured. Yet, often one wants to learn more about the problem than only how to predict. The interpretation of the...

We propose a computer intensive method for linear dimension reduction which minimizes the classification error directly. Simulated annealing (Bohachevsky et al 1986) as a modern optimization technique is used to solve this problem effectively. This approach easily allows to incorporate user...