  Linear Discriminant Analysis (LDA) is commonly used for dimensionality
reduction in pattern recognition and statistics. It is a supervised method that
aims to find the most discriminant space of reduced dimension that can be
further used for classification. In this work, we present a Grassmann Iterative
LDA method (GILDA) that is based on Proxy Matrix Optimization (PMO). PMO makes
use of automatic differentiation and stochastic gradient descent (SGD) on the
Grassmann manifold to arrive at the optimal projection matrix. Our results show
that GILDAoutperforms the prevailing manifold optimization method.
