GazePlotter
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Transitions & Markov Metrics

Transition metrics describe the dynamics of eye movement, mapping how visual attention shifts from one Area of Interest (AOI) to another. In GazePlotter, these metrics are formulated as a 2D matrix representing transitions from a source AOI (row) to a target AOI (column).

Output Shape and Projections Translation

All transition metrics naturally output an aoi-pair-matrix (an N×N grid, where N is the number of active AOIs). However, using GazePlotter’s projection algebra, you can translate this raw matrix into vectors or scalars, making transition metrics consumable by almost any visualization in the workspace.

1. Translating Matrix to Vector (aoi-vector)

You can project the N×N matrix into an array of values per AOI:

  • Self-Transitions (matrix-diagonal): Extracts the diagonal elements, representing the rate or probability of remaining within the same AOI on consecutive steps.
  • Outgoing Transitions (matrix-row): Extracts a single row for a specific source AOI. This outputs the transitions from that AOI to all other active AOIs.
  • Incoming Transitions (matrix-col): Extracts a single column for a specific target AOI. This outputs the transitions from all active AOIs to that target AOI.

Visualizer Compatibility: Projecting a transition matrix into a vector allows you to select it in the AOI Comparison plot (non-windowed) or the AOI Timeline (windowed).

2. Translating Matrix to Scalar (scalar)

You can reduce the N×N matrix into a single numerical value:

  • Specific Transition Cell (matrix-cell): Extracts the value of a specific directional link (e.g., AOI A > AOI B).
  • Matrix Aggregate (matrix-aggregate): Reduces the entire grid using a reducer (sum, mean, max, or min), optionally excluding diagonal self-transitions.

Visualizer Compatibility: Projecting a transition matrix into a scalar allows you to select it in the Metric Correlation plot (non-windowed) or the Metric Timeline plot (windowed).

Metric Recipes

GazePlotter provides four transition-based recipes:

1. Transitions (transitionCount)

The raw count of gaze shifts from a source AOI to a target AOI.

  • Raw Shape: aoi-pair-matrix
  • Unit: count
  • Measurement class: Extensive (additive total). Across participants, counts default to a cohort total (the group’s combined transitions) but can also be shown as a per-participant mean. Because counts are summable, reducing across matrix cells also allows a total or an average (not just max/min).

2. Transition Probability (transitionProbability)

The conditional probability of transitioning to a target AOI given that the gaze is currently on a source AOI.

  • Raw Shape: aoi-pair-matrix
  • Unit: %
  • Measurement class: Intensive (normalized). The average probability matrix is computed across participants; a cohort total is not meaningful. Because a probability matrix is not additive, reducing across matrix cells offers only max and min.
  • Step Parameter (step): k-step Markov transition probability.
    • step = 1: Direct probability matrix P.
    • step = k > 1: Computes the matrix power P^k, representing the probability of arriving at target AOI after exactly k transitions.

3. Mean Transition Dwell (transitionDwellMean)

The average duration (in milliseconds) spent in a source AOI before transitioning to a target AOI.

  • Raw Shape: aoi-pair-matrix
  • Unit: ms
  • Measurement class: Intensive (normalized). A per-participant mean dwell, averaged across participants. For a group total, use Transitions or a summable dwell metric instead.

4. Transition Relative Frequency (transitionRelativeFrequency)

The percentage share of all transitions occurring between specific AOI pairs, normalized against the total number of transitions across the entire stimulus.

  • Raw Shape: aoi-pair-matrix
  • Unit: %
  • Measurement class: Intensive (normalized). Each cell is a per-participant share, averaged across participants; summing shares across participants or cells is not meaningful.

Parameters

All transition recipes support a common Mode parameter:

  • Fixation Mode (mode: 'fixation'): Counts every consecutive fixation pair. If a participant makes three fixations in AOI A and then one in AOI B, the system registers two self-transitions (A > A) and one outgoing transition (A > B).
  • Visit Mode (mode: 'visit'): Collapses consecutive same-AOI fixations first. In the example above, the three fixations in AOI A are collapsed into a single visit. The system only registers one transition: Visit A > Visit B. Self-transitions (A > A) are eliminated.