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

Joydeep Chandra, Satyam Kumar Navneet, Yong Zhang

TL;DR

This work introduces a novel framework applying Topological Data Analysis specifically persistent homology to model users' longitudinal posting histories as trajectories in semantic embedding space, and proposes Semantic Recovery Velocity (SRV), a novel metric quantifying the rate users move away from initial distress-focused posts in embedding space.

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.

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

TL;DR

This work introduces a novel framework applying Topological Data Analysis specifically persistent homology to model users' longitudinal posting histories as trajectories in semantic embedding space, and proposes Semantic Recovery Velocity (SRV), a novel metric quantifying the rate users move away from initial distress-focused posts in embedding space.

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.
Paper Structure (24 sections, 4 equations, 1 figure, 1 table)

This paper contains 24 sections, 4 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Computational Mental Health Analysis
  4. Topological Data Analysis in NLP and HCI
  5. Trajectory Analysis in Mental Health
  6. Methods
  7. Data Collection and Preprocessing
  8. Semantic Embedding and Trajectory Construction
  9. Persistent Homology Computation
  10. Topological Feature Extraction
  11. Semantic Recovery Velocity (SRV)
  12. Multi-Proxy Validation
  13. Results
  14. Topological Signatures of Trajectory Patterns
  15. SRV Validation
  16. ...and 9 more sections

Figures (1)

  • Figure 1: Overview of the Topology of Recovery pipeline. Reddit posts from r/depression (n = 15,847 users, 2018–2020) are encoded with MentalBERT and projected to 3D via UMAP. Vietoris–Rips filtration then extracts three topological features — Loop Persistence (LP), Flare Index (FI), and Semantic Recovery Velocity (SRV), which are validated against five proxies using a Random Forest classifier and translated into HCI design implications. Trajectory vignettes (right) illustrate two archetypal recovery patterns: looping (high LP) and flaring (high FI).System architecture of The Topology of Recovery. The pipeline proceeds through six phases: (1) Data Collection — 15,847 longitudinal Reddit users (r/depression, ≥10 posts, ≥90-day span) are extracted via the Pushshift API; (2) Semantic Embedding — posts are encoded with MentalBERT (768-dim) and projected to 3D via UMAP; (3) Topological Data Analysis — Vietoris–Rips filtration computes persistent homology (H₀, H₁, H₂), yielding persistence diagrams and Betti curves via giotto-tda; (4) Feature Extraction — three interpretable topological features are derived: Loop Persistence (LP, rumination cycles), Flare Index (FI, growth expansion), and Semantic Recovery Velocity (SRV, directional momentum toward recovery); (5) Multi-Proxy Validation — features are validated against five proxies (self-report, behavioral signals, volunteer annotation, negative controls, and temporal holdout) using a Random Forest classifier (combined accuracy: 78.3%); and (6) Design Implications — trajectory patterns inform four HCI design directions: reflective visualizations, adaptive resources, peer connection, and progress tracking. Representative trajectory vignettes illustrate the looping (high LP) and flaring (high FI) recovery archetypes.