# Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)

arXiv: https://arxiv.org/abs/2006.11220 · HTML: https://mlsanity.com/paper/2006.11220/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 13 of 13)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach](https://mlsanity.com/paper/2403.07954/) (2024)
- [Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming](https://mlsanity.com/paper/2409.07794/) (2024)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [Signal Processing on the Permutahedron: Tight Spectral Frames for Ranked Data Analysis](https://mlsanity.com/paper/2103.04150/) (2021)
- [Joint Network Topology Inference via Structured Fusion Regularization](https://mlsanity.com/paper/2103.03471/) (2021)
- [Frames for Graph Signals on the Symmetric Group: A Representation Theoretic Approach](https://mlsanity.com/paper/2203.03036/) (2022)
- [Large Graph Signal Denoising with Application to Differential Privacy](https://mlsanity.com/paper/2209.02043/) (2022)
- [Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs](https://mlsanity.com/paper/2506.01404/) (2025)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)
- [Lightweight Transformer for EEG Classification via Balanced Signed Graph Algorithm Unrolling](https://mlsanity.com/paper/2510.03027/) (2025)
- [Hierarchical Clustering and Signal Denoising on Digraphs](https://mlsanity.com/paper/2609.34670/) (2026)

## Abstract (arXiv)

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal processing and machine learning tasks. Designing collections of building block signals -- or more formally, dictionaries of atoms -- that specifically account for the underlying graph structure as well as any available representative training signals has been an active area of research over the last decade. In this article, we survey a particular class of dictionaries called localized spectral graph filter frames, whose atoms are created by localizing spectral patterns to different regions of the graph. After showing how this class encompasses a variety of approaches from spectral graph wavelets to graph filter banks, we focus on the two main questions of how to design the spectral filters and how to select the center vertices to which the patterns are localized. Throughout, we emphasize computationally efficient methods that ensure the resulting transforms and their inverses can be applied to data residing on large, sparse graphs. We demonstrate how this class of transform methods can be used in signal processing tasks such as denoising and non-linear approximation, and provide code for readers to experiment with these methods in new application domains.