# Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations

## TL;DR

This paper presents a new unsupervised co-learning approach for manifolds with group actions, leveraging multiple irreducible representations to improve tasks like nearest neighbor search and community detection.

## Contribution

It introduces a novel representation theoretic framework for manifold co-learning across irreducible group representations, enhancing unsupervised learning on structured manifolds.

## Key findings

- Improved robustness in nearest neighbor search.
- Enhanced community detection in cryo-electron microscopy images.
- Effective use of multiple irreducible representations for manifold learning.

## Abstract

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.