  We present sketched linear discriminant analysis, an iterative randomized
approach to binary-class Gaussian model linear discriminant analysis (LDA) for
very large data. We harness a least squares formulation and mobilize the
stochastic gradient descent framework. Therefore, we obtain a randomized
classifier with performance that is very comparable to that of full data LDA
while requiring access to only one row of the training data at a time. We
present convergence guarantees for the sketched predictions on new data within
a fixed number of iterations. These guarantees account for both the Gaussian
modeling assumptions on the data and algorithmic randomness from the sketching
procedure. Finally, we demonstrate performance with varying step-sizes and
numbers of iterations. Our numerical experiments demonstrate that sketched LDA
can offer a very viable alternative to full data LDA when the data may be too
large for full data analysis.
