# Quiver Laplacians and Feature Selection

arXiv: https://arxiv.org/abs/2404.06993 · HTML: https://mlsanity.com/paper/2404.06993/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 41 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 4 of 4)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [The Geometry of Synchronization Problems and Learning Group Actions](https://mlsanity.com/paper/1610.09051/) (2016)
- [Quiver Signal Processing (QSP)](https://mlsanity.com/paper/2010.11525/) (2020)

## Built on by (most cited first, 2 of 2)

- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)

## Abstract (arXiv)

The challenge of selecting the most relevant features of a given dataset arises ubiquitously in data analysis and dimensionality reduction. However, features found to be of high importance for the entire dataset may not be relevant to subsets of interest, and vice versa. Given a feature selector and a fixed decomposition of the data into subsets, we describe a method for identifying selected features which are compatible with the decomposition into subsets. We achieve this by re-framing the problem of finding compatible features to one of finding sections of a suitable quiver representation. In order to approximate such sections, we then introduce a Laplacian operator for quiver representations valued in Hilbert spaces. We provide explicit bounds on how the spectrum of a quiver Laplacian changes when the representation and the underlying quiver are modified in certain natural ways. Finally, we apply this machinery to the study of peak-calling algorithms which measure chromatin accessibility in single-cell data. We demonstrate that eigenvectors of the associated quiver Laplacian yield locally and globally compatible features.