# Learning Optimal Graph Filters for Clustering of Attributed Graphs

arXiv: https://arxiv.org/abs/2211.04634 · HTML: https://mlsanity.com/paper/2211.04634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 79 references that are in the map.
- First posted on arXiv 9 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Label Efficient Semi-Supervised Learning via Graph Filtering](https://mlsanity.com/paper/1901.09993/) (2019)
- [Community Detection in Networks with Node Attributes](https://mlsanity.com/paper/1401.7267/) (2014)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Signal Recovery on Graphs: Variation Minimization](https://mlsanity.com/paper/1411.7414/) (2014)
- [GraphHop: An Enhanced Label Propagation Method for Node Classification](https://mlsanity.com/paper/2101.02326/) (2021)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [Compressive Spectral Clustering](https://mlsanity.com/paper/1602.02018/) (2016)
- [Adaptive Diffusions for Scalable Learning over Graphs](https://mlsanity.com/paper/1804.02081/) (2018)
- [Filter Design for Autoregressive Moving Average Graph Filters](https://mlsanity.com/paper/1711.09086/) (2017)
- [Non-Bayesian Estimation Framework for Signal Recovery on Graphs](https://mlsanity.com/paper/2005.01952/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application](https://mlsanity.com/paper/2508.16633/) (2025)

## Abstract (arXiv)

Many real-world systems can be represented as graphs where the different entities in the system are presented by nodes and their interactions by edges. An important task in studying large datasets with graphical structure is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on combining these two complementary sources of information through graph convolutional networks and graph filtering. However, these methods are mostly limited to lowpass filtering and do not explicitly learn the filter parameters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we learn the parameters of Finite Impulse Response (FIR) and Autoregressive Moving Average (ARMA) graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem, focusing on learning interpretable graph filters that are optimal for the given data and that maximize the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art methods.