109 citations · 243 across the 25 of their papers we have counts for
5 papers · 1 filter
Fractional Diffusion Maps
Harbir Antil, Tyrus Berry, John Harlim
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in…
Applications of topological graph theory to -manifold learning
Tyrus Berry, Steven Schluchter
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in , we may obtain a global representation as a cell complex with vertices giv…
Limits on reconstruction of dynamical networks
Jiajing Guan, Tyrus Berry, Timothy Sauer
An observability condition number is defined for physical systems modeled by network dynamics. Assuming the dynamical equations of the network are known and a noisy trajectory is o…
Correcting Observation Model Error in Data Assimilation
Franz Hamilton, Tyrus Berry, Timothy Sauer
Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted outp…
Spectral exterior calculus
Tyrus Berry, Dimitrios Giannakis
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the li…