Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations
This work addresses the challenge of learning manifolds with group actions, particularly for cryo-electron microscopy image analysis, though it appears incremental as it builds on existing fibre bundle structures.
The paper tackles the problem of unsupervised manifold learning by introducing a co-learning paradigm that leverages multiple views from irreducible representations of a transformation group, resulting in drastically improved robust nearest neighbor search and community detection on rotation-invariant cryo-electron microscopy image analysis.
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.