#### Date of Award

2014

#### Degree Type

Thesis

#### Degree Name

Master of Science in Industrial and Systems Engineering

#### Department

Mechanical, Industrial and Systems Engineering

#### First Advisor

Manbir Sodhi

#### 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 increase as expected by a Wiener process. This suggests that as the distance between time samples increases, at some point, the differences in position will no longer follow a Wiener process. The additional parameter assessment comparison for the Wiener process showed that in both the horizontal and vertical directions, the variances of the distributions differed significantly between the control and n-back runs. The variances for the n-back runs were consistently larger than those for the control runs. This provides support to hypothesis 2.

Additional analyses regarding whether the gaze path followed a random walk were executed. The distribution of the angle or direction of movement was analyzed. In comparison to a uniform distribution, when saccades were removed, 60% of the 53 runs failed to reject the null hypothesis. For the data with saccades, only 21% of the 53 runs failed to reject the null hypothesis. Thus, there was a significant difference in the distributions of the angle of eye movement between the data with and without saccades. When saccades were removed, there is more support for the gaze path following a random walk, compared to when saccades are included in the assessment.

This research and resulting conclusions are important in starting to explain the involuntary eye movements which occur when a participant is singularly focused. These results provide strong evidence that this underlying movement can be represented as a Wiener process. For any experiment considering eye movements, the inherent movement of the eyes should be considered in the analysis.

#### Recommended Citation

Wasserman, Staci A., "MODELING THE FOCUS OF ATTENTION AS A RANDOM PROCESS" (2014). *Open Access Master's Theses.* Paper 344.

https://digitalcommons.uri.edu/theses/344

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p9_nback3_data.csv (344 kB)