Dimensionality Reduction of Dynamics on Lie Manifolds via Structure-Aware Canonical Correlation Analysis
Year: 2023
Type: preprint
Abstract: Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, 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. Structural impositions in constrained systems increase when applying group structure, converting them into Lie manifolds. The range of their applications is very wide and includes the important case of robotic tasks. Canonical Correlation Analysis (CCA) can construct a hierarchical sequence of maximal correlations of up to two paired data sets in these Euclidean spaces. We present a method to generalize this concept to Lie Manifolds and demonstrate its efficacy through the substantial improvements it achieves in making structure-consistent predictions about changes in the state of a robotic hand.
Source: arXiv (Cornell University)
Authors: Chung, Wooyoung, Polani, Daniel, Tiomkin, Stas
Institutions: San Jose State University, University of Hertfordshire
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G2134488847
OpenAlex ID: W4388843387