# Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis

arXiv: https://arxiv.org/abs/2109.13573 · HTML: https://mlsanity.com/paper/2109.13573/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2021.

## 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)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guarantees](https://mlsanity.com/paper/2305.01379/) (2023)
- [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)
- [Blind Extraction of Equitable Partitions from Graph Signals](https://mlsanity.com/paper/2203.05407/) (2022)
- [Sampling Transferable Graph Neural Networks with Limited Graph Information](https://mlsanity.com/paper/2410.16593/) (2024)
- [Cramer-Rao Bounds for Laplacian Matrix Estimation](https://mlsanity.com/paper/2504.04576/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

This paper treats a blind detection problem to identify the central nodes in a graph from filtered graph signals. Unlike prior works which impose strong restrictions on the data model, we only require the underlying graph filter to satisfy a low pass property with a generic low-rank excitation model. We treat two cases depending on the low pass graph filter's strength. When the graph filter is strong low pass, i.e., it has a frequency response that drops sharply at the high frequencies, we show that the principal component analysis (PCA) method detects central nodes with high accuracy. For general low pass graph filter, we show that the graph signals can be described by a structured factor model featuring the product between a low-rank plus sparse factor and an unstructured factor. We propose a two-stage decomposition algorithm to learn the structured factor model via a judicious combination of the non-negative matrix factorization and robust PCA algorithms. We analyze the identifiability conditions for the model which lead to accurate central nodes detection. Numerical experiments on synthetic and real data are provided to support our findings. We demonstrate significant performance gains over prior works.