Noisy Graph Patterns via Ordered Matrices

2026-01-16

AI Summary

This work addresses the challenge of identifying and defining typical graph patterns—such as cliques and bicliques—in real-world graph data corrupted by noise. To this end, the authors propose a noise-robust approach based on adjacency matrix reordering and Moran’s I statistic. The method first employs Moran’s I to derive an optimal node ordering that transforms latent graph patterns into well-structured rectangular submatrices. It then combines exact algorithms with heuristic strategies to efficiently decompose noisy patterns. Furthermore, a noise-aware motif simplification technique is introduced to facilitate effective visualization. Extensive experiments on multiple real-world datasets demonstrate that the proposed method reliably identifies and visualizes graph patterns under noisy conditions, confirming its effectiveness and practical utility.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

The high-level structure of a graph is a crucial ingredient for the analysis and visualization of relational data. However, discovering the salient graph patterns that form this structure is notoriously difficult for two reasons. (1) Finding important patterns, such as cliques and bicliques, is computationally hard. (2) Real-world graphs contain noise, and therefore do not always exhibit patterns in their pure form. Defining meaningful noisy patterns and detecting them efficiently is a currently unsolved challenge. In this paper, we propose to use well-ordered matrices as a tool to both define and effectively detect noisy patterns. Specifically, we represent a graph as its adjacency matrix and optimally order it using Moran's $I$. Standard graph patterns (cliques, bicliques, and stars) now translate to rectangular submatrices. Using Moran's $I$, we define a permitted level of noise for such patterns. A combination of exact algorithms and heuristics allows us to efficiently decompose the matrix into noisy patterns. We also introduce a novel motif simplification that visualizes noisy patterns while explicitly encoding the level of noise. We showcase our techniques on several real-world data sets.

Problem

• noisy graph patterns
• graph structure
• pattern detection
• adjacency matrix
• Moran's I

Innovation

• noisy graph patterns
• ordered adjacency matrix
• Moran's I
• matrix decomposition
• motif simplification