MODELING THE FOCUS OF ATTENTION AS A RANDOM PROCESS

Abstract

This research investigates the feasibility of modeling visual attention (as represented through eye movements) as a stochastic process. A stochastic model of attention would provide a foundation for research involving probabilistic predictions of attention allocation which could be used in a variety of domains. The following hypotheses are examined as part of this research. The visual trace of participants when asked to fixate on a single point can be modeled as a stochastic process (Supported). The visual trace of participants will fluctuate when performing an additional cognitive task, but can still be modeled stochastically with additional parameter considerations (Supported). In order to determine whether attention could be modeled as a stochastic process, eye-tracking data were collected and analyzed. The experiment contains only a single focal point with no distractors. The goal of this experiment is to determine how the eyes move when attention is singularly focused. This experiment does not attempt to determine how attention is captured or distracted, but rather to understand the foundational elements of attention that can be ascertained from the inherent movement of the eyes. To determine whether the data could be modeled as a stochastic process, different tests are used to compare the empirical cumulative distribution function to the hypothesized theoretical distribution. It was hypothesized that the saccade occurrences follow a Poisson process, but only 46% of the 52 runs provided support that the data could be modeled as a Poisson process. There was no significant difference between the control and n-back runs. Overall, there is not enough evidence to support that the saccades follow a Poisson process. The Wiener process and random walk are hypothesized to relate to the gaze pattern or visual trace. For the Wiener process, the length of movement in the horizontal and vertical directions was assessed for normality. The hypothesis that the data followed a Wiener process was supported by 100% of the 53 runs in both the horizontal and vertical directions. Thus, this data was able to be modeled as a stochastic process, specifically a Wiener process, which supported hypothesis 1. This analysis was extended to consider whether the distribution changed as the differences in position increased to two samples, three samples, four samples, five samples, and ten samples. As the number of time samples between eye position difference calculations increased, the results still strongly supported that the data followed a normal distribution. However, the variance proportions did not