# Koopman Subspace Pruning in Reproducing Kernel Hilbert Spaces via Principal Vectors

arXiv: https://arxiv.org/abs/2604.01459 · HTML: https://mlsanity.com/paper/2604.01459/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [Revisiting the Nystrom Method for Improved Large-Scale Machine Learning](https://mlsanity.com/paper/1303.1849/) (2013)
- [Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems](https://mlsanity.com/paper/2111.14889/) (2021)
- [Estimating Koopman operators with sketching to provably learn large scale dynamical systems](https://mlsanity.com/paper/2306.04520/) (2023)
- [An overview of Koopman-based control: From error bounds to closed-loop guarantees](https://mlsanity.com/paper/2509.02839/) (2025)
- [Another look at Residual Dynamic Mode Decomposition in the regime of fewer Snapshots than Dictionary Size](https://mlsanity.com/paper/2403.05891/) (2024)
- [Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2506.15782/) (2025)
- [Modeling Nonlinear Control Systems via Koopman Control Family: Universal Forms and Subspace Invariance Proximity](https://mlsanity.com/paper/2307.15368/) (2023)
- [Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models](https://mlsanity.com/paper/2311.13033/) (2023)
- [Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds](https://mlsanity.com/paper/2603.15091/) (2026)
- [A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors](https://mlsanity.com/paper/2603.29001/) (2026)

## Abstract (arXiv)

Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the operator. Yet, existing techniques are largely restricted to Euclidean settings. To bridge this gap, this paper presents an approach for computing principal angles and vectors to enable Koopman subspace pruning within a Reproducing Kernel Hilbert Space (RKHS) geometry. We first outline an exact computational routine, which is subsequently scaled for large datasets using randomized Nystrom approximations. Based on these foundations, we introduce the Kernel-SPV and Approximate Kernel-SPV algorithms for targeted subspace refinement via principal vectors. Simulation results validate our approach.