GazePlotter
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Recurrence Quantitative Analysis (RQA)

Recurrence Quantitative Analysis (RQA) is a non-linear analysis method used to study the dynamical characteristics of scanpaths. By plotting a participant’s fixation sequence against itself, GazePlotter identifies recurring visual patterns, periodic revisitations, and dwelling behaviors.

The Recurrence Plot Foundation

RQA metrics are computed from an underlying Recurrence Plot, which is a binary matrix R where:

R(i, j) = 1   if fixation i and fixation j land on the same area (AOI / Euclidean distance)
R(i, j) = 0   otherwise

For details on the visualizer that displays this raw matrix, see Recurrence Plot.

Output Shape and Projections Translation

All RQA metrics naturally output a scalar value representing a global property of the recurrence sequence. Because the raw output is already scalar, no further dimensional projection is required.

1. Scalar Passthrough (scalar)

You can pass the scalar value through directly to analyze the participant’s recurrence rate, determinism, or laminarity:

  • Identity (identity-scalar): Passes the computed RQA percentage through directly.

Visualizer Compatibility: Passing the raw scalar through allows you to select RQA metrics in the Metric Correlation plot (non-windowed, aggregate) or the Metric Timeline plot (windowed, timeseries). RQA metrics cannot be projected to vectors or matrices, so they are not selectable in plots like AOI Comparison or Transition Matrix.

Measurement class: All three RQA metrics are intensive (normalized rates in 0–100%). Each describes one participant’s whole scanpath, so across participants they are averaged; a cohort total is not meaningful.

Metric Recipes

GazePlotter provides three RQA metrics:

1. Recurrence Rate (rqaRec)

The density of recurrence points in the recurrence plot, representing the percentage of fixation pairs that land on the same AOI.

  • Raw Shape: scalar
  • Unit: %
  • Windowing: Supported (fixation-windowed).
  • Scientific Meaning: A general index of how repetitive the scanpath is. Higher recurrence rates indicate a gaze pattern that repeatedly returns to previously visited regions.

2. Determinism (rqaDet)

The percentage of recurrence points that form diagonal lines parallel to the main diagonal (with a minimum line length of 2).

  • Raw Shape: scalar
  • Unit: %
  • Windowing: Supported (fixation-windowed).
  • Scientific Meaning: Measures the predictability or regularity of the scanpath. A high determinism score indicates that the participant repeatedly executes the same multi-step sequences of AOI visits (e.g., A > B > C > A > B > C).

3. Laminarity (rqaLam)

The percentage of recurrence points that form vertical line segments (with a minimum line length of 2).

  • Raw Shape: scalar
  • Unit: %
  • Windowing: Supported (fixation-windowed).
  • Scientific Meaning: Indicates the presence of laminar states, where the gaze remains trapped in a specific region or alternates rapidly between overlapping areas. High laminarity points to detailed local inspection or visual dwelling.

Parameters

All RQA metrics share a common parameter:

  • Include Off-AOI Fixations (include_no_aoi):
    • false (default): Off-AOI fixations (those not falling inside any defined AOI) are skipped entirely. The sequence contains only AOI visits.
    • true: Off-AOI fixations participate in the sequence, represented by the noAoiSlot sentinel. This allows the system to analyze recurrences that occur outside structured boundaries.

Ordinal Windowing (windowUnit: 'fixations')

Unlike duration-based metrics which slide across time in milliseconds, RQA metrics slice the sequence of events using ordinal windows (measured in fixations):

  • Window Size: The number of consecutive fixations to include in each analysis bin (e.g., 50 fixations).
  • Step Size: The fixation shift between consecutive bins (e.g., 1 fixation).
  • Inner Leaf: The inner projection must be identity-scalar, yielding a scalar-timeseries output shape.

Midpoint Membership: The scan runtime uses midpoint-in-window gating (frame.midpointInWindow) to assign each fixation to its respective ordinal bins.