  Sparse coding is a common approach to learning local features for object
recognition. Recently, there has been an increasing interest in learning
features from spatio-temporal, binocular, or other multi-observation data,
where the goal is to encode the relationship between images rather than the
content of a single image. We provide an analysis of multi-view feature
learning, which shows that hidden variables encode transformations by detecting
rotation angles in the eigenspaces shared among multiple image warps. Our
analysis helps explain recent experimental results showing that
transformation-specific features emerge when training complex cell models on
videos. Our analysis also shows that transformation-invariant features can
emerge as a by-product of learning representations of transformations.
