Eye movements and information geometry.

Area of Science:

• Computational Neuroscience
• Computer Vision
• Statistical Modeling

Background:

• Human visual system utilizes eye movements for information gathering, categorized into fixation movements and saccades.
• Previous models often employ random walk or heavy-tailed distributions (e.g., Lévy flights) to describe eye movement patterns.
• A gap exists in applying extreme value statistics to model the step lengths of eye movements.

Purpose of the Study:

• To demonstrate that eye movement step lengths between fixations are accurately modeled by generalized Pareto distributions (GPDs).
• To explore the application of information geometry and Fisher information matrices to GPDs of eye movement data.
• To develop a feature vector for characterizing GPDs using geometric properties and test its efficacy in observer identification.

Main Methods:

• Applied extreme value statistics to analyze eye tracking data, fitting step lengths to generalized Pareto distributions (GPDs).
• Utilized information geometry to define a Riemann manifold for GPDs and computed the Fisher information matrix.
• Engineered a feature vector based on GPD parameters and Fisher information matrix properties; employed a naive Bayes classifier for observer identification.

Main Results:

• Empirical analysis confirmed that GPDs provide a strong fit for measured eye movement step lengths.
• The Fisher information matrix for GPDs was computed, and its geometric properties were used to create descriptive feature vectors.
• A naive Bayes classifier utilizing eigenvalues of the Fisher information matrix achieved high accuracy in identifying individual observers.

Conclusions:

• Generalized Pareto distributions offer a robust statistical framework for modeling eye movement step lengths.
• Information geometry provides a powerful lens for analyzing the statistical properties of these distributions.
• The developed feature vectors and classification approach show promise for objective observer identification from eye tracking data.