  Large-sample data became prevalent as data acquisition became cheaper and
easier. While a large sample size has theoretical advantages for many
statistical methods, it presents computational challenges. Sketching, or
compression, is a well-studied approach to address these issues in regression
settings, but considerably less is known about its performance in
classification settings. Here we consider the computational issues due to large
sample size within the discriminant analysis framework. We propose a new
compression approach for reducing the number of training samples for linear and
quadratic discriminant analysis, in contrast to existing compression methods
which focus on reducing the number of features. We support our approach with a
theoretical bound on the misclassification error rate compared to the Bayes
classifier. Empirical studies confirm the significant computational gains of
the proposed method and its superior predictive ability compared to random
sub-sampling.
