  Quadratic discriminant analysis (QDA) is a widely used classification
technique. Based on a training dataset, each class in the data is characterized
by an estimate of its center and shape, which can then be used to assign unseen
observations to one of the classes. The traditional QDA rule relies on the
empirical mean and covariance matrix. Unfortunately, these estimators are
sensitive to label and measurement noise which often impairs the model's
predictive ability. Robust estimators of location and scatter are resistant to
this type of contamination. However, they have a prohibitive computational cost
for large scale industrial experiments. We present a novel QDA method based on
a recent real-time robust algorithm. We additionally integrate an anomaly
detection step to classify the most atypical observations into a separate class
of outliers. Finally, we introduce the label bias plot, a graphical display to
identify label and measurement noise in the training data. The performance of
the proposed approach is illustrated in a simulation study with huge datasets,
and on real datasets about diabetes and fruit.
