Dimensionality Reduction of Dynamics on Lie Groups via Structure-Aware Canonical Correlation Analysis
Publication Date
1-1-2024
Document Type
Conference Proceeding
Publication Title
Proceedings of the American Control Conference
DOI
10.23919/ACC60939.2024.10644415
First Page
439
Last Page
446
Abstract
Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, relia-bility, and generalization outside of the training sample. The stronger the structural properties, the more effective these improvements become. Manifolds are a powerful nonlinear generalization of Euclidean space for modeling finite dimensions. When additionally assuming that the manifold carries (Lie) group structure, this imposes a drastically stricter global constraint. The range of their applications is very wide and includes the important case of robotic tasks. We apply this idea to Canonical Correlation Analysis (CCA). In traditional CCA one constructs a hierarchical sequence of maximal correlations of up to two paired data sets in Euclidean spaces. We here generalize the CCA concept to respect the structure of Lie groups and demonstrate its efficacy through the substantial improvements it achieves in making structure-consistent pre-dictions about changes in the state of a robotic hand.
Funding Number
2246221
Funding Sponsor
National Science Foundation
Department
Computer Engineering
Recommended Citation
Wooyoung Chung, Daniel Polani, and Stas Tiomkin. "Dimensionality Reduction of Dynamics on Lie Groups via Structure-Aware Canonical Correlation Analysis" Proceedings of the American Control Conference (2024): 439-446. https://doi.org/10.23919/ACC60939.2024.10644415
