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

TL;DR

This paper introduces a novel topological data analysis framework using persistent homology to map and analyze individual mental health recovery trajectories in online communities, revealing patterns linked to improvement.

Contribution

It presents a new TDA-based methodology for modeling mental health journeys, with interpretable topological signatures and practical implications for adaptive mental health platforms.

Findings

Topological signatures predict self-reported improvement with 78.3% accuracy.

Loops indicate stagnation, flares suggest exploration of new coping strategies.

The approach outperforms sentiment baselines in predicting mental health improvement.

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.