Comparative Linear Classification Splicing

The conventional Fisher linear classification analysis has been investigated by numerous researchers and this has led to different modification or splicing due to non- robustness when the assumptions are violated and also when the data set contains influential observations.  This paper adduced a winsorized procedure to robustify the probability base classification approach.  The comparative classification performance of the Fisher linear classification analysis and its spliced versions when the data set are contaminated are investigated. The simulation results revealed that the robust Fisher's approach based on the minimum covariance determinant estimates outperformed the other procedures; a good competitor to this technique is the winsorized probability base classification technique. Though, the robust Fisher's technique using the minimum covariance determinant estimates breakdown for mixture contamination. On a general note, the conventional Fisher's approach and the probability base technique performed comparable

Influence of observations on the misclassification probability in quadratic discriminant analysis.

In this paper it is analyzed how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the quality of the associated classification rule. Focus is more on the effect on the future misclassification rate, than on the influence on the parameters of the quadratic discriminant rule. The expression for the influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.Applications; Classification; Data; Diagnostics; Discriminant analysis; Functions; Influence function; Misclassification probability; Outliers; Partial influence functions; Probability; Quadratic discriminant analysis; Quality; Robust covariance estimation; Robust regression; Training;

Classification efficiencies for robust linear discriminant analysis.

Linear discriminant analysis is typically carried out using Fisher’s method. This method relies on the sample averages and covariance matrices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it has been proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher’s method. In this paper relative classification efficiencies of the robust procedures with respect to the classical method are computed. Second order influence functions appear to be useful for computing these classification efficiencies. It turns out that, when using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. These findings are confirmed by finite sample simulations.Classification efficiency; Discriminant analysis; Error rate; Fisher rule; Influence function; Robustness;