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Identifying Fixations in Gaze Data via Inner Density and Optimization

Author

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  • Andrew C. Trapp

    (Robert A. Foisie Business School, Worcester Polytechnic Institute, Worcester, Massachusetts 01609; Data Science Program, Worcester Polytechnic Institute, Worcester, Massachusetts 01609)

  • Wen Liu

    (Data Science Program, Worcester Polytechnic Institute, Worcester, Massachusetts 01609;)

  • Soussan Djamasbi

    (Robert A. Foisie Business School, Worcester Polytechnic Institute, Worcester, Massachusetts 01609;)

Abstract

Eye tracking is an increasingly common technology with a variety of practical uses. Eye-tracking data, or gaze data, can be categorized into two main events: fixations represent focused eye movement, indicative of awareness and attention, whereas saccades are higher-velocity movements that occur between fixation events. Common methods to identify fixations in gaze data can lack sensitivity to peripheral points and may misrepresent positional and durational properties of fixations. To address these shortcomings, we introduce the notion of inner density for fixation identification, which concerns both the duration of the fixation and the proximity of its constituent gaze points. Moreover, we demonstrate how to identify fixations in a sequence of gaze data by optimizing for inner density. After decomposing the clustering of a temporal gaze data sequence into successive regions (chunks), we use nonlinear and linear 0–1 optimization formulations to identify the densest fixations within a given data chunk. Our approach is parametrized by a unique constant that adjusts the degree of desired density, allowing decision makers to have fine-tuned control over density during the process. Computational experiments on real data sets demonstrate the efficiency of our approach and its effectiveness in identifying fixations with greater density than existing methods, thereby enabling the refinement of key gaze metrics such as fixation duration and fixation center.

Suggested Citation

  • Andrew C. Trapp & Wen Liu & Soussan Djamasbi, 2019. "Identifying Fixations in Gaze Data via Inner Density and Optimization," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 459-476, July.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:3:p:459-476
    DOI: 10.1287/ijoc.2018.0859
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    References listed on IDEAS

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    1. Wu, Tai-Hsi, 1997. "A note on a global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 220-223, August.
    2. Saglam, Burcu & Salman, F. Sibel & Sayin, Serpil & Turkay, Metin, 2006. "A mixed-integer programming approach to the clustering problem with an application in customer segmentation," European Journal of Operational Research, Elsevier, vol. 173(3), pages 866-879, September.
    3. Andrew C. Trapp & Oleg A. Prokopyev, 2010. "Solving the Order-Preserving Submatrix Problem via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 387-400, August.
    4. Andrew Trapp & Oleg A. Prokopyev & Stanislav Busygin, 2010. "Finding checkerboard patterns via fractional 0–1 programming," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 1-26, July.
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    Cited by:

    1. Liu, Wen & Trapp, Andrew C. & Djamasbi, Soussan, 2021. "Outlier-Aware, density-Based gaze fixation identification," Omega, Elsevier, vol. 102(C).

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