Eye Movement Analysis: A Kernel Density Estimation Approach for Saccade Direction and Amplitude

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Abstract
Eye movements are important indicators of problem-solving or solution strategies and are recorded using eye-tracking technologies. As they reveal how viewers interact with presented information during task processing, their analysis is crucial for educational research. Traditional methods for analyzing saccades, such as histograms or polar diagrams, are limited in capturing patterns in direction and amplitude. To address this, we propose a kernel density estimation approach that explicitly accounts for the data structure: for the circular distribution of saccade direction, we use the von Mises kernel, and for saccade amplitude, a Gaussian kernel. This yields continuous probability distributions that not only improve accuracy of representations but also model the underlying distribution of eye movements. This method enables the identification of strategies used during task processing and reveals the connections to the underlying cognitive processes. It allows for a deeper understanding of information processing during learning. By applying our new method to an empirical dataset, we uncovered differences in solution strategies that conventional techniques could not reveal. The insights gained can contribute to the development of more effective teaching methods, better tailored to the individual needs of learners, thereby enhancing their academic success.

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