  We introduce a novel co-learning paradigm for manifolds naturally equipped
with a group action, motivated by recent developments on learning a manifold
from attached fibre bundle structures. We utilize a representation theoretic
mechanism that canonically associates multiple independent vector bundles over
a common base manifold, which provides multiple views for the geometry of the
underlying manifold. The consistency across these fibre bundles provide a
common base for performing unsupervised manifold co-learning through the
redundancy created artificially across irreducible representations of the
transformation group. We demonstrate the efficacy of the proposed algorithmic
paradigm through drastically improved robust nearest neighbor search and
community detection on rotation-invariant cryo-electron microscopy image
analysis.
