Advancing eye movement analysis through compositional modeling: A new perspective on Yarbus' classic study

Eye-tracking metrics based on Areas of Interest (AOIs) often represent the relative allocation of visual attention across stimulus regions. Compositional data analysis (CoDA) provides a mathematically principled framework for analyzing such data and enables the application of a wide range of multivariate statistical methods through their representation in log-ratio coordinates. This study demonstrates the utility of CoDA in AOI-based eye-tracking research using a large-scale replication of Yarbus' classic "Unexpected Visitor" experiment. Eye movements of 144 participants were recorded with a high-precision eye-tracker while they viewed Ilja Repin's painting under seven tasks adapted from Yarbus. Total fixation durations within seven AOIs were analyzed either as absolute measures (classical approach) or as compositions representing the relative distribution of viewing time across AOIs. Descriptive CoDA techniques (compositional means, variation matrices, and ternary plots) together with multivariate methods in log-ratio coordinates (principal component analysis, hierarchical clustering, and compositional MANOVA) reproduce the qualitative patterns described by Yarbus and subsequent replications, confirming that task demands strongly shape the relative allocation of attention. Linear discriminant analysis further shows that the task being performed can be inferred from eye-movement patterns with accuracy above the chance level. The paper is conceived as a tutorial introduction to CoDA in eye-tracking research. The compositional framework is particularly appropriate when AOI metrics represent proportions or when total viewing time is fixed by design, while under unconstrained viewing time, it provides a complementary perspective to classical analyses.