LERM

LERM (Laplacian Eigenmaps of Recurrence Matrices) [@James2024] is a nonlinear method that operates in the system’s reconstructed phase space rather than on raw values. The pipeline is: time-delay embedding → recurrence matrix → Laplacian eigenmaps over sliding windows → Fisher Information signal → transition detection as confidence-interval crossings of that signal.

When to use

Best for: Dynamical regime changes where the climate system shifts state without a large amplitude jump, transitions that are invisible to amplitude-based methods like the Augmented KS Test.

Limitation: The pipeline is more complex and computationally heavier than the other two methods.

Reference

James, A., Emile-Geay, J., Malik, N., & Khider, D. (2024). Detecting Paleoclimate Transitions With Laplacian Eigenmaps of Recurrence Matrices (LERM). Paleoceanography and Paleoclimatology. https://doi.org/10.1029/2023PA004700

Tutorial

See the LERM Validation notebook for a worked example.