Statistical Image Analysis of Eye Movement Trajectories in Multi-Attribute Decision Making

Abstract

Eye-tracking studies of decision making have traditionally relied on Area-of-Interest (AOI) statistics, scan-path metrics, fixation measures, and transition analyses. Although these approaches have provided important insights, AOI-based methods require predefined semantic spatial regions and may not fully characterize the broader spatial organization of gaze behavior. This study proposes an image-based framework in which eye movement trajectories are represented as grayscale images on a regular spatial grid and analyzed using established image-analysis techniques, including texture analysis, Fourier analysis, wavelet decomposition, and singular value decomposition (SVD). Non-negative matrix factorization (NMF) was also examined as a candidate method, but was not included in the final integrated analysis because its contribution was limited in the present sample. The remaining heterogeneous image-derived features were integrated using a Tucker-1-based framework and examined using principal component analysis (PCA) and probabilistic PCA (PPCA). The framework was demonstrated using eye-tracking data from insurance decision tasks involving multiple pieces of decision-relevant information. The first principal component showed strong and consistent correlations with conventional fixation count and fixation duration across both insurance tasks, supporting its interpretation as a global fixation-intensity dimension, whereas higher-order components showed substantially weaker associations with these conventional measures. Bootstrap analyses further indicated that the exact PPCA dimensionality was sensitive to sampling variability, although relatively high-dimensional latent structures were consistently supported. Overall, the proposed framework provides a complementary representation of gaze behavior that does not require predefined semantic AOI boundaries and may capture both conventional fixation-related information and additional spatial or structural characteristics of eye movement trajectories.