  Quadratic and Linear Discriminant Analysis (QDA/LDA) are the most often
applied classification rules under normality. In QDA, a separate covariance
matrix is estimated for each group. If there are more variables than
observations in the groups, the usual estimates are singular and cannot be used
anymore. Assuming homoscedasticity, as in LDA, reduces the number of parameters
to estimate. This rather strong assumption is however rarely verified in
practice. Regularized discriminant techniques that are computable in
high-dimension and cover the path between the two extremes QDA and LDA have
been proposed in the literature. However, these procedures rely on sample
covariance matrices. As such, they become inappropriate in presence of cellwise
outliers, a type of outliers that is very likely to occur in high-dimensional
datasets. In this paper, we propose cellwise robust counterparts of these
regularized discriminant techniques by inserting cellwise robust covariance
matrices. Our methodology results in a family of discriminant methods that (i)
are robust against outlying cells, (ii) cover the gap between LDA and QDA and
(iii) are computable in high-dimension. The good performance of the new methods
is illustrated through simulated and real data examples. As a by-product,
visual tools are provided for the detection of outliers.
