Higher-Order Network Structure Inference: A Topological Approach to Network Selection

2025-10-06

AI Summary

Existing threshold selection methods for complex networks suffer from two key limitations: (1) reliance on heuristic rules and high sensitivity to parameter tuning, and (2) neglect of higher-order interactions involving three or more nodes. To address these issues, this paper proposes a robust threshold optimization framework grounded in Topological Data Analysis (TDA). Methodologically, it introduces persistent homology—applied for the first time to quantify the stability of network topological features—and integrates user-defined hyperparameter constraints to guide threshold search on co-occurrence networks via higher-order structural priors. The core contribution lies in selecting thresholds based on higher-order topological features (e.g., 2-simplices and beyond), rather than pairwise edges alone, thereby enhancing both robustness and interpretability. Experiments on scientometric concept networks demonstrate that the resulting networks exhibit strong resilience to parameter perturbations, preserve ternary and higher-order relational structures significantly better than baselines, and admit clear topological semantics.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations. Threshold selection often relies on heuristic methods or trial and error due to large parameter spaces and unclear optimization criteria, leading to sensitivity where small parameter variations produce significant changes in network structure. Moreover, most approaches focus on pairwise relationships between nodes, overlooking critical higher-order interactions involving three or more nodes. We introduce a systematic thresholding algorithm that leverages topological data analysis to identify optimal network parameters by accounting for higher-order structural relationships. Our method uses persistent homology to compute the stability of homological features across the parameter space, identifying parameter choices that are robust to small variations while preserving meaningful topological structure. Hyperparameters allow users to specify minimum requirements for topological features, effectively constraining the parameter search to avoid spurious solutions. We demonstrate the approach with an application in the Science of Science, where networks of scientific concepts are extracted from research paper abstracts, and concepts are connected when they co-appear in the same abstract. The flexibility of our approach allows researchers to incorporate domain-specific constraints and extends beyond network thresholding to general parameterization problems in data analysis.

Problem

• Systematic threshold selection for robust network structure extraction
• Addressing limitations of pairwise methods by capturing higher-order interactions
• Optimizing network parameters using topological data analysis techniques

Innovation

• Leveraging topological data analysis for network thresholding
• Using persistent homology to assess homological feature stability
• Incorporating hyperparameters to constrain parameter search space