TY - JOUR
T1 - Unsupervised co-learning on G-manifolds across irreducible representations
AU - Fan, Yifeng
AU - Gao, Tingran
AU - Zhao, Zhizhen
N1 - Acknowledgement: This work is supported in part by the National Science Foundation DMS-185479 and DMS-1854831.
PY - 2019
Y1 - 2019
N2 - We introduce a novel co-learning paradigm for manifolds naturally admitting an action of a transformation group G, 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 our proposed algorithmic paradigm through drastically improved robust nearest neighbor identification in cryo-electron microscopy image analysis and the clustering accuracy in community detection.
AB - We introduce a novel co-learning paradigm for manifolds naturally admitting an action of a transformation group G, 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 our proposed algorithmic paradigm through drastically improved robust nearest neighbor identification in cryo-electron microscopy image analysis and the clustering accuracy in community detection.
UR - http://www.scopus.com/inward/record.url?scp=85090177584&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85090177584&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85090177584
SN - 1049-5258
VL - 32
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019
Y2 - 8 December 2019 through 14 December 2019
ER -