Watching AI evolve.
Understanding what comes next.
The current source text is the original text and can be switched to the Chinese translation.
arXiv:2611.06990v1 Announce Type: new Abstract: Data arising in scientific applications often exhibits complex nonlinear structure. Identifying and parameterizing said nonlinearities can enable better modeling, enhance predictive analysis, data interpolation, denoising, and anomaly detection. In this paper, we develop theoretical and computational methods to detect and parametrize Euclidean point cloud data lying near a wedge sum of tori. Specifically, we use persistent cohomology and cup products to identify the distinct toroidal components, and on each component, we optimize over low-energy multivariate trigonometric polynomials for best data fit. The ensuing optimization problem reduces to generalized ridge regression, which can be solved efficiently via standard techniques. We demonstrate the utility of the proposed framework in both synthetic and real datasets, including interpolation of low frame-rate recurrent videos, attractor recovery in quasiperiodic dynamical systems, and the parametrization of gene-space cycle data for parasites and humans.
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .
The content of this article comes from arXiv stat.ML，Copyright belongs to the original author and publisher.
Read the original ↗Discuss the facts and ideas with respect. Comments appear after moderation.
Loading comments…