# Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes

arXiv: https://arxiv.org/abs/2210.14758 · HTML: https://mlsanity.com/paper/2210.14758/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2022.

## Built on by (most cited first, 8 of 8)

- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [Graph Classification Gaussian Processes via Hodgelet Spectral Features](https://mlsanity.com/paper/2410.10546/) (2024)
- [Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes](https://mlsanity.com/paper/2505.23160/) (2025)
- [Multiscale Hodge Scattering Networks for Data Analysis](https://mlsanity.com/paper/2311.10270/) (2023)
- [Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations](https://mlsanity.com/paper/2505.10877/) (2025)
- [Topological Graph Signal Compression](https://mlsanity.com/paper/2308.11068/) (2023)

## Abstract (arXiv)

This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles, etc.) and perfectly localized on the dual domain (e.g., a set of frequencies). These signals are obtained as the principal eigenvectors of a matrix built from proper localization operators acting over topology and frequency domains. Then, we suggest a principled procedure to build dictionaries of topological Slepians, which theoretically provide non-degenerate frames. Finally, we evaluate the effectiveness of the proposed topological Slepian dictionary in two applications, i.e., sparse signal representation and denoising of edge flows.