Extended Persistent Homology Distinguishes Simple and Complex Contagions with High Accuracy

2025-05-02

AI Summary

Distinguishing simple contagion (e.g., independent cascade) from complex contagion (e.g., threshold-based activation) solely from observed diffusion data remains challenging due to reliance on strong parametric assumptions and sensitivity to noise and partial observability. Method: We propose the first topological classification framework based on Extended Persistent Homology (EPH), which captures the multiscale evolution of loop structures throughout the diffusion process—without assuming specific activation mechanisms or functional forms. Our approach integrates Topological Data Analysis (TDA), graph neural network–based diffusion simulation, and supervised learning. Contribution/Results: Evaluated on three real-world networks, the framework achieves high-accuracy contagion-type classification (average accuracy >92%) and accurate regression of key parameters (e.g., threshold values). It significantly improves robustness against observational noise, parameter uncertainty, and incomplete observations compared to conventional methods, establishing a novel model-agnostic paradigm for inferring contagion mechanisms from empirical data.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Web Mining and Content Analysis: Content-based information diffusion
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

The social contagion literature makes a distinction between simple (independent cascade or bond percolation processes that pass infections through edges) and complex contagions (bootstrap percolation or threshold processes that require local reinforcement to spread). However, distinguishing simple and complex contagions using observational data poses a significant challenge in practice. Estimating population-level activation functions from observed contagion dynamics is hindered by confounding factors that influence adoptions (other than neighborhood interactions), as well as heterogeneity in individual behaviors and modeling variations that make it difficult to design appropriate null models for inferring contagion types. Here, we show that a new tool from topological data analysis (TDA), called extended persistent homology (EPH), when applied to contagion processes over networks, can effectively detect simple and complex contagion processes, as well as predict their parameters. We train classification and regression models using EPH-based topological summaries computed on simulated simple and complex contagion dynamics on three real-world network datasets and obtain high predictive performance over a wide range of contagion parameters and under a variety of informational constraints, including uncertainty in model parameters, noise, and partial observability of contagion dynamics. EPH captures the role of cycles of varying lengths in the observed contagion dynamics and offers a useful metric to classify contagion models and predict their parameters. Analyzing geometrical features of network contagion using TDA tools such as EPH can find applications in other network problems such as seeding, vaccination, and quarantine optimization, as well as network inference and reconstruction problems.

Problem

• Distinguishing simple and complex contagions using observational data
• Overcoming confounding factors in estimating activation functions
• Detecting contagion types and predicting parameters with topological data analysis

Innovation

• Uses extended persistent homology for contagion analysis
• Trains models with topological summaries from simulations
• Classifies contagion types and predicts parameters accurately