# A topological data analysis method for revealing dynamic changes in psychotherapy microprocesses

## TL;DR

This paper introduces a new method to study how psychotherapy changes over time by analyzing dynamic patterns in microprocesses.

## Contribution

The novel Temporal Mapper method uses topological data analysis to detect and model dynamic features in psychotherapy microprocesses.

## Key findings

- Therapist warmth stabilizes interpersonal states within and between sessions.
- Confrontation ruptures stabilize states within sessions but cause instability across sessions.
- Temporal Mapper reveals fine-grained dynamic patterns in psychotherapy data.

## Abstract

Understanding moment-to-moment therapeutic change is critical for advancing psychological interventions, yet existing tools rarely capture these dynamics. Dynamical systems theory offers a transtheoretical framework for modeling how therapeutic microprocesses shift and stabilize, but few methods can quantitatively link features such as stable states (“attractors”) and shifts (“transitions”) with empirical data, especially for high-dimensional systems when governing equations are unknown or unresolvable. We introduce Temporal Mapper, a topological data analysis (TDA) method that detects these features and represents their organization as attractor transition networks. As a proof-of-concept, we apply Temporal Mapper to psychotherapy microprocess data examining interpersonal behaviors and alliance ruptures. Our analyses revealed that therapist warmth stabilized dyadic interpersonal states within and between sessions, whereas confrontation ruptures stabilized dyadic interpersonal states within sessions but diversified and destabilized them across sessions. Beyond this example, Temporal Mapper offers a generalizable approach for uncovering fine-grained dynamic patterns, analyzing multimodal data of psychotherapy process, and identifying mechanisms of change at the system level to inform more effective interventions.