Skip to main content

Exploring Gaze Re-Inspection Dynamics with Running Recurrence Quantification Analysis (RRQA)

Vojtechovska
/
Research
/
Publications
/
Publication detail

Paper introduces RRQA to track gaze re-inspection dynamics per fixation, improving temporal resolution of RQA for complex gaze behavior analysis.

Read the article ResearchGate
Year
2025
Type
Conference paper
Original language
EN
Proceedings
Proceedings of the 2025 Symposium on Eye Tracking Research and Applications
Authors
M. Vojtechovska, M. Muczková, S. Popelka

Contribution

  1. Formalization of Running Recurrence Quantification Analysis (RRQA) as an incremental (fixation-by-fixation) extension of Recurrence Quantification Analysis (RQA) for modeling temporal re-inspection dynamics in eye-movement sequences.

  2. Definition of an algorithmic framework for continuously updating recurrence plots and standard RQA metrics (REC, DET, LAM, CORM) as growing vectors rather than aggregate descriptors, enabling time-resolved characterization of gaze structure.

  3. Integration of multiple recurrence definitions—fixed spatial distance and Areas of Interest (AOI-based recurrence)—to support both fine-grained spatial similarity and task-driven region-based analysis within a unified RRQA pipeline.

  4. Design of complementary visualization paradigms (Worm, Fence, and Horizon plots) for comparative and exploratory analysis of temporally evolving recurrence metrics across participants and stimuli.

  5. Conceptual framework for interpreting joint trajectories of recurrence metrics (e.g., DET×LAM, LAMₕ×LAMᵥ) as indicators of evolving gaze strategies and re-engagement patterns under varying task constraints.

  6. Implementation of a browser-based analytical system architecture for local, privacy-preserving RRQA computation and interactive parameter control, supporting reproducible exploratory analysis of fixation sequences.

Abstract

Gaze behavior provides key insights into cognitive processes such as attention, perception, and decision-making. Traditional eye-tracking metrics—such as fixation durations—capture meaningful patterns but overlook re-fixation dynamics, which signal shifts in gaze strategies. Recurrence Quantification Analysis (RQA) detects such patterns but aggregates data across entire tasks, obscuring temporal variations. Sliding Window RQA (SWRQA) tracks recurrence over time, yet fixed window sizes struggle with short fixation sequences and long-span recurrences, limiting suitability for gaze data. To address these limitations, we present Running RQA (RRQA). This proof-of-concept computes standard RQA metrics at each fixation, enabling fine-grained temporal tracking of Recurrence Rate (REC), Determinism (DET), Laminarity (LAM), and Center of Recurrence Mass (CORM). We introduce three visualization techniques to map changes in RRQA metrics for per-fixation, multi-participant comparisons. An open-source web application enables researchers to upload, analyze, and explore gaze data with RRQA visualizations interactively, facilitating detailed investigations of re-examination behavior: https://osf.io/ptfe7/.

Questions addressed

What is recurrence quantification analysis in eye-tracking research?

Recurrence quantification analysis (RQA) is a nonlinear time-series method that quantifies how often and in what temporal structures gaze returns to previously viewed locations. In eye-tracking, RQA captures re-fixation patterns that are not visible through standard metrics such as fixation duration or transition counts.

Why is traditional RQA limited for analyzing gaze behavior over time?

Traditional RQA aggregates recurrence metrics across an entire fixation sequence, producing single summary values per trial or task. Such aggregation masks mid-task changes in viewing strategy, attentional shifts, or decision phases that unfold during interaction.

How does running recurrence quantification analysis differ from sliding-window approaches?

Running recurrence quantification analysis updates recurrence metrics at every fixation by progressively expanding the reference sequence rather than using a fixed-size window. Sliding-window approaches can miss long-span re-fixations or short strategic returns when window size is poorly matched to gaze dynamics.

What recurrence metrics are typically tracked in a fixation-level RQA framework?

Commonly tracked metrics include Recurrence Rate (frequency of returns), Determinism (repetition of fixation sequences), Laminarity (sustained or repeated attention to locations), and Center of Recurrence Mass (temporal concentration of re-fixations). Tracking these metrics per fixation yields time-resolved profiles instead of single values.

How is spatial recurrence defined when applying RQA to gaze data?

Spatial recurrence can be defined either by fixed spatial distance between fixation coordinates or by shared membership in predefined areas of interest. Distance-based definitions capture fine-grained visual detail re-checking, while AOI-based definitions emphasize goal-driven revisits to semantically meaningful regions.

What visualization strategies can support interpretation of dynamic RQA metrics in eye-tracking data?

Dynamic RQA metrics can be visualized by aligning metric values to fixation indices, producing time-resolved profiles that unfold with the gaze sequence. Sequential and layered visual encodings allow inspection of how recurrence structures evolve, rather than collapsing behavior into aggregate summaries.

Citation

Vojtechovska, M., Muczková, M., & Popelka, S. (2025). Exploring Gaze Re-Inspection Dynamics with Running Recurrence Quantification Analysis (RRQA). Proceedings of the 2025 Symposium on Eye Tracking Research and Applications, 7. https://doi.org/10.1145/3715669.3725875

See other publications