# Blind Community Detection from Low-rank Excitations of a Graph Filter

arXiv: https://arxiv.org/abs/1809.01485 · HTML: https://mlsanity.com/paper/1809.01485/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2018.

## Built on by (most cited first, 9 of 9)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [A Comprehensive Review of Community Detection in Graphs](https://mlsanity.com/paper/2309.11798/) (2023)
- [Criteria-Aware Graph Filtering: Extremely Fast Yet Accurate Multi-Criteria Recommendation](https://mlsanity.com/paper/2502.09046/) (2025)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Online Network Source Optimization with Graph-Kernel MAB](https://mlsanity.com/paper/2307.03641/) (2023)
- [Learning Graph from Smooth Signals under Partial Observation: A Robustness Analysis](https://mlsanity.com/paper/2509.14887/) (2025)
- [Memory Is No Longer a Bottleneck: Memory-Efficient Graph Filtering for Scalable Collaborative Filtering](https://mlsanity.com/paper/2606.21540/) (2026)
- [Blind Extraction of Equitable Partitions from Graph Signals](https://mlsanity.com/paper/2203.05407/) (2022)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on a `low-pass' property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical experiments demonstrate that our approach is effective.