Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise
This work addresses a domain-specific challenge in dynamical systems analysis, but it is incremental as it compares existing methods without introducing new ones.
The study tackled the problem of aligning manifolds from double pendulum dynamics with noise, finding that semi-supervised feature-level local alignment methods achieved smaller alignment errors, greater robustness to noise, and faster performance compared to other methods.
This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.