基于不可约表示的$\mathcal{G}$ -流形上的无监督协同学习
Unsupervised Co-Learning on $\mathcal{G}$-Manifolds Across Irreducible Representations
摘要：
我们介绍了一种新的共同学习的流形自然配备了一个组的行动，最近的发展动态学习流形从附加的纤维束结构的动机。我们利用表示理论的机制，规范关联多个独立的向量束在一个共同的基础流形，这提供了多个视图的几何基础流形。这些纤维束之间的一致性为通过在变换群的不可约表示之间人为创建的冗余来执行无监督流形共同学习提供了一个共同的基础。我们证明了所提出的算法范例，通过大幅提高强大的最近邻搜索和社区发现旋转不变的冷冻电子显微镜图像分析的有效性。
英文摘要：
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.
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