Linear representations have frequently been used in image analysis
but are seldom found to be optimal in specific applications. We
propose a stochastic gradient algorithm for finding optimal linear
representations of images for use in appearance-based object
recognition. Using the nearest neighbor classifier, we specify a
recognition performance function with continuous derivatives. By
formulating the problem of finding optimal linear representations
as that of optimization on a Grassmann manifold, we first derive
an intrinsic gradient flow on the Grassmannian and later
generalize it to a stochastic gradient algorithm for optimization.
We present several experimental results to establish the
effectiveness of this algorithm.