Modeling and Analysis of Fish Interaction Networks under Projected Visual Stimuli

TL;DR

The previously proposed network estimation model is extended by introducing a stimulus term, which enables the model to capture how individuals react to and propagate externally projected visual stimuli within the group, and the resulting framework allows simultaneous estimation of inter-individual and stimulus-related interaction strengths.

Abstract

This paper addresses the estimation of a dynamic interaction network, a network of influence among individuals, under projected visual stimuli to quantify the influences of inter-individual interactions and external stimuli on collective behavior. Building upon our previously proposed network estimation model, which assumes a Boids-type model and employs a sparse regression framework to infer inter-individual influence networks from trajectory data, we extend the formulation by introducing a stimulus term. This enables the model to capture how individuals react to and propagate externally projected visual stimuli within the group. The resulting framework allows simultaneous estimation of inter-individual and stimulus-related interaction strengths. We also introduce entropy-based indices to capture the possible biases of individuals' influence. Our experiments with fish schools under projector-based visual stimuli demonstrate the effectiveness of the proposed indices in quantifying schooling behavior and identifying influential individuals within the group, serving as the basis for real-time, interpretable metrics of collective dynamics.

Figures (5)

• Figure 1: Distributions of time-averaged normalized individual coefficients for (a) coordination, (b) stimulus, and (c) autonomous components under conditions C and S1–S3. Statistical significance was assessed using the Kruskal-Wallis test, followed by Dunn's post-hoc test with Bonferroni correction (*$p < 0.05$, **$p < 0.01$, ***$p < 0.001$).
• Figure 2: Time-series of model-derived indices under stimulus condition S3: coordination strength $S_{\mathrm{att}}$ (solid blue), stimulus responsiveness $S_{\mathrm{stim}}$ (solid orange), and the sum of autonomous components $\sum_i w_{ii}$ (dashed line).
• Figure 3: Individual influence analysis for condition S3. (a) Temporal variation of $I_i$. (b) Network snapshots where node size is proportional to $I_i$ and edge thickness reflects weight $w_{ij}$ (thresholded for clarity).
• Figure 4: Estimated weight matrices $w_{ij}$ sampled every 60 frames (1 s) from frame 1180 to 1480. Diagonal and off-diagonal elements represent autonomous and inter-individual coordination (attraction) coefficients, respectively.
• Figure 5: Normalized entropy of the time-averaged relative influence ($H_{\mathrm{influ}}$) and stimulus responsiveness ($H_{\mathrm{stim}}$) across the group. Statistical notation follows Fig. \ref{['fig:individual_coefficients']}.