The Topology of Recovery: Using Persistent Homology to Map Individual Mental Health Journeys in Online Communities

2026-02-27

AI Summary

This study addresses the limitation of existing approaches in capturing the dynamic process of individual mental health recovery, which typically offer only static snapshots of population-level trends. To overcome this, the work introduces topological data analysis (TDA) into human-computer interaction research on mental health, leveraging persistent homology to model users’ longitudinal posting trajectories in semantic embedding space. Topological features—such as loops and dispersion—are employed to identify distinct recovery patterns, and a novel metric, Semantic Recovery Velocity (SRV), is proposed to quantify the extent to which users move away from their initial distress states. Evaluated on 15,847 user trajectories from r/depression, the topological features achieve 78.3% accuracy in predicting self-reported improvement, significantly outperforming sentiment-analysis-based baselines, thereby offering a new foundation for interpretable, adaptive mental health intervention platforms.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Humans and AI: Intelligent User Interfaces
• Data Mining & Knowledge Management: Conversational Systems for Recommendation & Retrieval

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Topic discovery and tracking

Abstract

Understanding how individuals navigate mental health challenges over time is critical yet methodologically challenging. Traditional approaches analyze community-level snapshots, failing to capture dynamic individual recovery trajectories. We introduce a novel framework applying Topological Data Analysis (TDA) specifically persistent homology to model users'longitudinal posting histories as trajectories in semantic embedding space. Our approach reveals topological signatures of trajectory patterns: loops indicate cycling back to similar states (stagnation), while flares suggest exploring new coping strategies (growth). We propose Semantic Recovery Velocity (SRV), a novel metric quantifying the rate users move away from initial distress-focused posts in embedding space. Analyzing 15,847 r/depression trajectories and validating against multiple proxies, we demonstrate topological features predict self-reported improvement with 78.3% accuracy, outperforming sentiment baselines. This work contributes: (1) a TDA methodology for HCI mental health research, (2) interpretable topological signatures, and (3) design implications for adaptive mental health platforms with ethical guardrails.

Problem

• mental health recovery
• individual trajectories
• online communities
• longitudinal analysis
• dynamic patterns

Innovation

• Topological Data Analysis
• Persistent Homology
• Semantic Recovery Velocity
• Mental Health Trajectories
• Online Communities