  This paper addresses the problem of object recognition given a set of images
as input (e.g., multiple camera sources and video frames). Convolutional neural
network (CNN)-based frameworks do not exploit these sets effectively,
processing a pattern as observed, not capturing the underlying feature
distribution as it does not consider the variance of images in the set. To
address this issue, we propose the Grassmannian learning mutual subspace method
(G-LMSM), a NN layer embedded on top of CNNs as a classifier, that can process
image sets more effectively and can be trained in an end-to-end manner. The
image set is represented by a low-dimensional input subspace; and this input
subspace is matched with reference subspaces by a similarity of their canonical
angles, an interpretable and easy to compute metric. The key idea of G-LMSM is
that the reference subspaces are learned as points on the Grassmann manifold,
optimized with Riemannian stochastic gradient descent. This learning is stable,
efficient and theoretically well-grounded. We demonstrate the effectiveness of
our proposed method on hand shape recognition, face identification, and facial
emotion recognition.
