  We develop projection pursuit for data that admit a natural representation in
matrix form. For projection indices, we propose extensions of the classical
kurtosis and Mardia's multivariate kurtosis. The first index estimates
projections for both sides of the matrices simultaneously, while the second
index finds the two projections separately. Both indices are shown to recover
the optimally separating projection for two-group Gaussian mixtures in the full
absence of any label information. We further establish the strong consistency
of the corresponding sample estimators. Simulations and a real data example on
hand-written postal code data are used to demonstrate the method.
