# Unsupervised Co-Learning on G-Manifolds Across Irreducible Representations

arXiv: https://arxiv.org/abs/1906.02707 · HTML: https://mlsanity.com/paper/1906.02707/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Joint Community Detection and Rotational Synchronization via Semidefinite Programming](https://mlsanity.com/paper/2105.06031/) (2021)
- [A Spectral Method for Joint Community Detection and Orthogonal Group Synchronization](https://mlsanity.com/paper/2112.13199/) (2021)
- [G-invariant diffusion maps](https://mlsanity.com/paper/2306.07350/) (2023)
- [The G-invariant graph Laplacian](https://mlsanity.com/paper/2303.17001/) (2023)
- [A Probabilistic Approach to Pose Synchronization for Multi-Reference Alignment with Applications to MIMO Wireless Communication Systems](https://mlsanity.com/paper/2511.03280/) (2025)

## Abstract (arXiv)

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.