Individual Topology Structure of Eye Movement Trajectories

TL;DR

This paper addresses the limitations of relying solely on macro-event statistics (fixations and saccades) for characterizing eye movement trajectories. It introduces topological data analysis features derived from persistent homology, applied across coordinate time series, heatmaps, and point clouds to capture whole-trajectory structure at multiple scales. Using 1D time-series filtrations and vectorizations of persistence diagrams, the approach yields robust, high-information descriptors that, in combination with traditional metrics, improve classification of eye-movement tasks on the GazeBase dataset. The results demonstrate that topological features are competitive on their own and synergistic with standard statistics, offering a practical, noise-robust pathway for analysis and potential clinical applications in diagnosing and understanding neural and cognitive conditions.

Abstract

Traditionally, extracting patterns from eye movement data relies on statistics of different macro-events such as fixations and saccades. This requires an additional preprocessing step to separate the eye movement subtypes, often with a number of parameters on which the classification results depend. Besides that, definitions of such macro events are formulated in different ways by different researchers. We propose an application of a new class of features to the quantitative analysis of personal eye movement trajectories structure. This new class of features based on algebraic topology allows extracting patterns from different modalities of gaze such as time series of coordinates and amplitudes, heatmaps, and point clouds in a unified way at all scales from micro to macro. We experimentally demonstrate the competitiveness of the new class of features with the traditional ones and their significant synergy while being used together for the person authentication task on the recently published eye movement trajectories dataset.

Figures (3)

• Figure 1: Vietoris-Rips clique complex generation process: from the separated point cloud elements to a high dimensional simplicial complex and corresponding persistence diagram on the right
• Figure 2: General pipeline description. First step is a specific data representation extraction. Second step is a topological features extraction. Third step consists in a vectorization of extracted topological features. And a final step is a machine learning algorithm realization
• Figure 3: One dimensional time series filtration process, which named lower star filtration with the corresponding simplicial complexes