# Matched Filters for Noisy Induced Subgraph Detection

arXiv: https://arxiv.org/abs/1803.02423 · HTML: https://mlsanity.com/paper/1803.02423/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2018.

## Built on by (most cited first, 6 of 6)

- [Clustered Graph Matching for Label Recovery and Graph Classification](https://mlsanity.com/paper/2205.03486/) (2022)
- [Subgraph nomination: Query by Example Subgraph Retrieval in Networks](https://mlsanity.com/paper/2101.12430/) (2021)
- [Gotta match 'em all: Solution diversification in graph matching matched filters](https://mlsanity.com/paper/2308.13451/) (2023)
- [Detection of Model-based Planted Pseudo-cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embedding](https://mlsanity.com/paper/2312.11054/) (2023)
- [Interconnected Kingdoms: Comparing 'A Song of Ice and Fire' Adaptations Across Media Using Complex Networks](https://mlsanity.com/paper/2410.05453/) (2024)
- [Approximate Subgraph Matching with Neural Graph Representations and Reinforcement Learning](https://mlsanity.com/paper/2603.18314/) (2026)

## Abstract (arXiv)

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to it Drosophila and human connectomes that this approach can achieve good performance.