# Hidden markov modeling of emotional state transitions in interactive installation art

## TL;DR

This paper uses hidden Markov models to analyze emotional states in a public art installation, showing that positive emotions are stable and dominant.

## Contribution

The novel application of HMMs to cross-sectional cultural data reveals latent emotional states and their stability in participatory art.

## Key findings

- Three distinct emotional states were identified: low/negative, moderately positive, and highly positive.
- Positive states were the most stable with high self-transition probability and longest dwell time.
- The stationary distribution showed 86.3% positivity, indicating a strong emotional attractor toward positive affect.

## Abstract

Interactive installation art provides a distinctive context for examining collective emotion, yet most prior studies have relied on laboratory or longitudinal data that are impractical in public cultural settings. This study applied Hidden Markov Models (HMMs) to self-reported well-being data from HappyHere, a participatory light installation at the National Galleries of Scotland. Despite the cross-sectional design, the HMM framework enabled inference of latent affective states and probabilistic differentiation patterns, stability, and convergence patterns. The results show four key findings. First, three qualitatively distinct latent states were identified: a low/negative cluster (M ≈ 1.5), a moderately positive cluster (M ≈ 3.5), and a ceiling-level, highly positive cluster (all M = 5.0), confirming clear differentiation (H1). Second, positive states proved the most stable, with the highest self-transition probability (0.875) and the longest dwell time (≈ 3.4 steps), supporting H2. Third, neutral states were comparatively unstable, showing the lowest self-transition probability (0.093) and a tendency to shift toward positivity, consistent with H3. Finally, the stationary distribution strongly favored positivity, with positive states Reaching 86.3%, neutral states 7.5%, and negative states 6.2%. Minor diurnal variation was observed, but effect sizes were negligible, confirming the enduring predominance of positivity (H4). The findings demonstrate that even cross-sectional cultural datasets can yield meaningful insights through probabilistic modelling. Positive affect emerged as the most stable and dominant attractor, underscoring the capacity of participatory art to regulate emotion and foster collective well-being.