# Design of graph filters and filterbanks

arXiv: https://arxiv.org/abs/1711.02046 · HTML: https://mlsanity.com/paper/1711.02046/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2017.

## Built on by (most cited first, 22 of 22)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networks](https://mlsanity.com/paper/2104.11846/) (2021)
- [Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs](https://mlsanity.com/paper/2304.11140/) (2023)
- [Graph Denoising with Framelet Regularizer](https://mlsanity.com/paper/2111.03264/) (2021)
- [MGC: A Complex-Valued Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/2110.07570/) (2021)
- [A Piece-wise Polynomial Filtering Approach for Graph Neural Networks](https://mlsanity.com/paper/2112.03499/) (2021)
- [Total Variation Graph Neural Networks](https://mlsanity.com/paper/2211.06218/) (2022)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Message Passing in Graph Convolution Networks via Adaptive Filter Banks](https://mlsanity.com/paper/2106.09910/) (2021)
- [Graph Neural Networks with Parallel Neighborhood Aggregations for Graph Classification](https://mlsanity.com/paper/2111.11482/) (2021)
- [LLM Online Spatial-temporal Signal Reconstruction Under Noise](https://mlsanity.com/paper/2411.15764/) (2024)
- [FiGURe: Simple and Efficient Unsupervised Node Representations with Filter Augmentations](https://mlsanity.com/paper/2310.01892/) (2023)
- [RSI-Net: Two-Stream Deep Neural Network for Remote Sensing Imagesbased Semantic Segmentation](https://mlsanity.com/paper/2109.09148/) (2021)
- [A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks](https://mlsanity.com/paper/2605.28578/) (2026)
- [Graphs as Tools to Improve Deep Learning Methods](https://mlsanity.com/paper/2110.03999/) (2021)
- [GSPRec: On Improving Item Representations in Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2505.11552/) (2025)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [SIEFormer: Spectral-Interpretable and -Enhanced Transformer for Generalized Category Discovery](https://mlsanity.com/paper/2602.13067/) (2026)

## Abstract (arXiv)

Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or dictionary more adapted to represent the information contained in them. The aim of this chapter is to review general concepts for the introduction of filters and representations of graph signals. We first begin by recalling the general framework to achieve that, which put the emphasis on introducing some spectral domain that is relevant for graph signals to define a Graph Fourier Transform. We show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators.