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API Reference#

Segmentation methods#

A concise overview of the segmentation algorithms available within the VisionToolkit library. For each method, a reference article that informed its implementation is cited.

Binary segmentation#

A BinarySegmentation object can be instantiated using the threshold-based methods included in this package:

  • I-VT: Performs binary segmentation based on a velocity threshold 84.
  • I-DiT: Performs binary segmentation using dispersion of consecutive data points within a temporal window—the dispersion metric is defined as the sum of the maximum and minimum differences between data coordinates 44.
  • I-DeT: Performs binary segmentation using a density criterion 59. This algorithm is a variant of the popular DBSCAN algorithm for fixation identification.
  • I-MST: Performs binary segmentation leveraging minimum spanning trees. Building on this tree representation, I-MST classifies each eye position into a fixation or a saccade based on point-to-point edge distance thresholds 44.
  • I-KF: Performs binary segmentation using a two-state Kalman filter which models the evolution of the eyes by a dynamic system with two states: position and velocity 46.

A BinarySegmentation object can also be instantiated using the learning-based segmentation methods included in this package:

  • I-HMM: Performs binary segmentation assuming a two-state (fixation and saccade) latent variable, where each state is characterized by a normal velocity distribution, while the switch between the different states is governed by a Markov jump process 84.
  • I-2MC: Performs binary segmentation using a 2-means clustering approach 35.
  • I-RF: Performs binary segmentation from a random forest classifier trained using a set of 14 features extracted from raw eye-gaze coordinates 100. This algorithm requires an annotated dataset for training.

Ternary segmentation#

A TernarySegmentation object can be instantiated using the threshold-based methods included in this package:

  • I-VVT: Performs ternary segmentation using two velocity thresholds 45.
  • I-VDT: Performs ternary segmentation using both a velocity and a dispersion threshold 45.
  • I-VMP: Performs ternary segmentation using eye movement patterns 2: the angles between the horizontal axis and the line formed by two successive gaze points are computed and then transformed into a set of points on the circumference of the unit circle. A Rayleigh score is then computed, and windows labeled consequently.
  • I-BDT: Performs ternary segmentation using a Bayesian decision theory approach 86. Building on physiological hypotheses, they introduced explicit formulas to compute likelihoods and priors of each eye movement that can be used to isolate event types.

A TernarySegmentation object can also be instantiated using the learning-based segmentation methods included in this package:

  • I-HOV: Performs ternary segmentation using a histogram of oriented velocities 29. The technique computes velocity-weighted angles between the inspected point and each preliminary or successive data point to produce a histogram that can be used as features to feed machine learning algorithms. This algorithm requires an annotated dataset for training.
  • I-CNN: Performs ternary segmentation using a convolutional neural network trained directly from raw eye data in order to isolate oculomotor events 30. This algorithm requires an annotated dataset for training.

Oculomotor processing#

A concise summary of the metrics included in the VisionToolkit library for characterizing detailed oculomotor behavior is provided. Each metric is accompanied by a reference to the source article that guided its implementation.

Signal-based features#

Frequency-based analysis

  • signal_periodogram(): Estimates power spectral density, using a periodogram 67, from raw eye-gaze signal.
  • signal_welch_periodogram(): Estimates power spectral density, using a Welch windowed periodogram 96, from eye-gaze signal.
  • signal_cross_spectral_density(): Estimates the cross power spectral density between two eye-gaze signals 67.
  • signal_welch_cross_spectral_density(): Estimates the cross power spectral density between two eye-gaze signals, according to Welch's method 67.
  • signal_coherency(): Derived from cross spectral density, assesses how two eye-gaze signals are related or the association between rhythmic activities contained in both signals 7.

Stochastic-based analysis

  • signal_MSD(): A measure of the deviation of the eye-gaze position with respect to a reference position over time 34. A useful tool that can be used to describe random walks.
  • signal_DACF(): A representation of the degree of similarity between the eye-gaze coordinate time series and a lagged version of itself over successive time intervals 34.
  • signal_DFA(): A method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes whose underlying statistics or dynamics are non-stationary 94.

Topological-based analysis

  • signal_persistence_size(): Computes the entropy of the size of the persistence diagram holes 17.
  • signal_persistence_robustness(): Computes the entropy of the robustness of the holes in the persistence diagram 17.
  • signal_betti_curve(): A one-dimensional function evaluating the Betti numbers obtained from a persistence diagram, at different levels of filtration 32.
  • signal_persistence_curve(): A one-dimensional function that summarizes the total persistence of topological holes obtained from a persistence diagram, at different levels of filtration 41.
  • signal_persistence_landscape(): The persistence landscape is used to map persistence diagrams into a function space 32.
  • signal_persistence_entropy(): The Shannon entropy of the collections of topological hole lifetimes obtained from a persistence diagram 41.

Fixation features#

Fixation temporal features

  • fixation_frequency(): Also referred to as fixation rate 82, this metric represents, given an eye-tracking recording session, the number of fixations occurring per second.
  • fixation_frequency_wrt_labels(): Given an eye-tracking recording session, computes the number of fixations per second 82, filtered according to a quality criterion to retain only validated fixations.
  • fixation_durations(): Given an eye-tracking recording session, computes the duration of each identified fixation sequence 82.
  • fixation_first_duration(): Given an eye-tracking recording session, computes the duration of the first fixation sequence identified 40.

Fixation spatial and stability features

  • fixation_centroids(): Given an eye-tracking recording session, computes centroid position of each identified fixation sequence by averaging coordinates of data samples composing individual fixations 82.
  • fixation_drift_displacements(): Given an eye-tracking recording session, computes distance between the starting and ending points of each identified fixation sequence 82.
  • fixation_drift_distances(): Given an eye-tracking recording session, for each identified fixation sequence, computes the sum of distances between each data sample within this fixation sequence 82.
  • fixation_mean_velocities(): Given an eye-tracking recording session, for each identified fixation sequence, computes the mean velocity of data samples within this fixation sequence 82.
  • fixation_drift_velocities(): Given an eye-tracking recording session, for each identified fixation sequence, computes the drift displacement normalized by the fixation duration 82.
  • fixation_BCEA(): Given an eye-tracking recording session, for each identified fixation sequence, computes the fixation bivariate contour ellipse area (BCEA) as the area of the elliptical contour that encompasses a given percentage of sample points identified as belonging to this fixation sequence 88.

Saccade features#

Saccade temporal features

  • saccade_frequency(): Also referred to as saccade rate 82, this metric represents, given an eye-tracking recording session, the number of saccades occurring per second.
  • saccade_frequency_wrt_labels(): Given an eye-tracking recording session, computes the number of saccades per second 82, filtered according to a quality criterion to retain only validated saccades.
  • saccade_durations(): Given an eye-tracking recording session, computes the duration of each identified saccade sequence 82.

Saccade kinematic features

  • saccade_amplitudes(): Given an eye-tracking recording session, computes distance between the starting and ending points of each identified saccade sequence 82.
  • saccade_travel_distances(): Given an eye-tracking recording session, for each identified saccade sequence, computes the sum of distances between each data sample within this saccade sequence 82.
  • saccade_efficiencies(): Given an eye-tracking recording session, for each identified saccade sequence, computes the ratio of saccadic amplitude over the distance traveled 82.
  • saccade_directions(): Given an eye-tracking recording session, for each identified saccade sequence, computes the deviation from the horizontal plane of the line connecting the start and end points of the saccade sequence 27.
  • saccade_successive_deviations(): Given an eye-tracking recording session, for each identified pair of successive saccade sequences, computes the angle formed by successive saccadic trajectories, where each saccade is modeled as a vector connecting its start and end points.
  • saccade_initial_directions(): Given an eye-tracking recording session, for each identified saccade sequence, computes the initial direction of the saccadic trajectory after a fixed number of data measures, e.g. after a number of timestamps corresponding to 20 ms 90.
  • saccade_initial_deviations(): Given an eye-tracking recording session, for each identified saccade sequence, computes the angle between the overall direction determined at the endpoint of the saccade and the initial direction after a fixed number of data measures, e.g. after a number of timestamps corresponding to 10 ms 87.
  • saccade_max_curvatures(): Given an eye-tracking recording session, for each identified saccade sequence, computes the maximum perpendicular distance from any point along the saccadic trajectory to the straight line connecting the start and end points of the saccade 61.
  • saccade_area_curvatures(): Given an eye-tracking recording session, for each identified saccade sequence, computes the area under the curve of the sampled saccadic trajectory, relative to the straight-line distance between the saccade's starting and ending points 61.

Saccade velocity and acceleration features

  • saccade_mean_velocities(): Given an eye-tracking recording session, for each identified saccade sequence, computes the mean velocity of data samples within this saccade sequence 82.
  • saccade_peak_velocities(): Given an eye-tracking recording session, for each identified saccade sequence, computes the peak velocity of data samples belonging to this saccade sequence 82.
  • saccade_acceleration_profiles(): Given an eye-tracking recording session, for each identified saccade sequence, computes the mean acceleration of data samples within this saccade sequence 82.
  • saccade_peak_accelerations(): Given an eye-tracking recording session, for each identified saccade sequence, computes the peak acceleration of data samples belonging to this saccade sequence 82.
  • saccade_accelerations(): Given an eye-tracking recording session, for each identified saccade sequence, computes the mean absolute acceleration during the acceleration phase of this saccade sequence, measured from the start point to the timestamp of peak acceleration 82.
  • saccade_decelerations(): Given an eye-tracking recording session, for each identified saccade sequence, computes the mean absolute acceleration during the deceleration phase of this saccade sequence, from the timestamp of peak acceleration to the endpoint 82.
  • saccade_skewness_exponents(): Given an eye-tracking recording session, for each identified saccade sequence, computes the shape parameter obtained by fitting a gamma function to the saccade velocity profile 16.

Saccade functional ratios

  • saccade_amp_dur_ratio(): Given an eye-tracking recording session, for each identified saccade sequence, computes the saccade amplitude over duration ratio 82.
  • saccade_peak_vel_amp_ratio(): Given an eye-tracking recording session, for each identified saccade sequence, computes the peak velocity over amplitude ratio 82.
  • saccade_peak_vel_dur_ratio(): Given an eye-tracking recording session, for each identified saccade sequence, computes the peak velocity over duration ratio 82.
  • saccade_peak_vel_vel_ratio(): Given an eye-tracking recording session, for each identified saccade sequence, computes the peak velocity over mean velocity ratio 82.
  • saccade_main_sequence(): Given an eye-tracking recording session, computes slopes of the amplitude/duration curve and the log peak velocity/log amplitude curve 6.

Saccade task features

  • saccade_latencies(): Given an eye-tracking recording session and a theoretical saccade sequence, computes the time difference between the onset of each theoretical saccade and the start time of each corresponding experimental saccade 98.
  • saccade_latency_quantiles(): Given an eye-tracking recording session and a theoretical saccade sequence, computes the set of saccade latencies, then computes quantiles of the latency distribution 91.
  • saccade_gain(): Given an eye-tracking recording session and a theoretical saccade sequence, computes the ratio between saccade and target amplitudes—i.e. the distances covered by a theoretical saccade and the distance covered by the saccade actually performed 38.

Smooth pursuit features#

Smooth pursuit temporal features

  • pursuit_frequency(): Also referred to as pursuit rate, this metric represents, given an eye-tracking recording session, the number of pursuit sequences occurring per second.
  • pursuit_frequency_wrt_labels(): Given an eye-tracking recording session, computes the number of smooth pursuits per second, filtered according to a quality criterion to retain only validated smooth pursuit sequences.
  • pursuit_durations(): Given an eye-tracking recording session, computes the duration of each identified smooth pursuit sequence.

Smooth pursuit kinematic features

  • pursuit_amplitudes(): Given an eye-tracking recording session, computes distance between the starting and ending points of each identified smooth pursuit sequence.
  • pursuit_travel_distances(): Given an eye-tracking recording session, for each identified smooth pursuit sequence, computes the sum of distances between each data sample within this pursuit sequence.
  • pursuit_efficiencies(): Given an eye-tracking recording session, for each identified smooth pursuit sequence, computes the ratio of pursuit amplitude over the distance traveled.

Smooth pursuit velocity features

  • pursuit_mean_velocities(): Given an eye-tracking recording session, for each identified smooth pursuit sequence, computes the mean velocity of data samples within this pursuit sequence.
  • pursuit_peak_velocities(): Given an eye-tracking recording session, for each identified smooth pursuit sequence, computes the peak velocity of data samples belonging to this pursuit sequence.

Smooth pursuit task features

  • pursuit_latency(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes the time difference between the onset of each theoretical smooth pursuit and the start time of each corresponding experimental pursuit 13. Computed as the abscissa of the intersection of two regression lines: the first line fits the pre-response baseline, and the second line fits the pursuit initiation velocity signal, recorded from a time window with duration of approximately 50 ms.
  • pursuit_initial_acceleration(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes the initial acceleration as the mean second-order position derivative of the saccade-free component extracted from the tracking response in the 100 ms interval immediately following pursuit onset 43.
  • pursuit_triangular_gain(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes the triangular gain as the ratio between eye and target mean velocities during each pursuit segment 79.
  • pursuit_sinusoidal_gain(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes the sinusoidal gain by fitting the eye velocity with a trigonometrical curve for each pursuit segment. The gain is then computed as the ratio between the peak velocity of the best fitting curve over the target's peak velocity 1.
  • pursuit_sinusoidal_phase(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes the phase of the velocity signal as the difference between the phases of the best-fitting velocity curve and the target's velocity profile 1.
  • pursuit_accuracy(): Estimates the proportion of time the smooth pursuit eye movement velocity is within the target velocity boundaries of less than 25% (adjustable) absolute error from the visual target velocity.
  • pursuit_error_entropy(): Given an eye-tracking recording session and a theoretical pursuit sequence, first computes the pursuit velocity error series as the difference between the experimental pursuit velocities and theoretical stimulus velocities. Then the approximate entropy 75 of the velocity error series is computed.
  • pursuit_cross_correlation(): Given an eye-tracking recording session and a theoretical pursuit sequence, computes normalized cross-correlation 77 between the experimental pursuit velocity and theoretical stimulus velocity signals.

Scanpath analysis#

A concise summary of the metrics included in the VisionToolkit library for characterizing scanpath trajectory. Each metric is accompanied by a reference to the source article that guided its implementation.

Single scanpath analysis#

Geometrical methods#

  • scanpath_BCEA(): Given a scanpath, computes the area of the elliptical contour that encompasses a given percentage of fixation centroids identified as belonging to this scanpath 88.
  • scanpath_k_coefficient(): Given a scanpath, derived by averaging the differences, for each fixation, between the standardized fixation duration and the standardized saccade amplitude of the subsequent saccade composing this scanpath 48.
  • scanpath_convex_hull(): Given a scanpath, computes the area of the smallest convex polygon that includes all fixations composing this scanpath 47.
  • scanpath_voronoi_cells(): Given a scanpath, computes the skewness and scale parameter of a gamma distribution by fitting it to the distribution of normalized Voronoi cell areas 72. A Voronoi cell is defined as the region containing all points in a plane that are closer to a specific fixation point than to any other fixation point within the scanpath.
  • scanpath_HFD(): Given a scanpath, computes the Higuchi fractal dimension of Hilbert curve distance series obtained from fixation centroids belonging to this scanpath 70.

Saliency-based method

  • scanpath_saliency_map(): Given a scanpath, or a list of scanpaths, computes a saliency map or heat map as a histogram where fixations from individual recordings, or aggregated across multiple observers, are counted at each pixel. Additionally, pixel activity is modeled as a Gaussian distribution, with the standard deviation determining the granularity of the heat map. The output is a map of relatively weighted pixels, where color or opacity reflects fixation density.

Recurrence quantification-based methods#

  • scanapath_RQA_recurrence_rate(): Given a recurrence plot computed from a single scanpath, derives the percentage of recurrent fixations, i.e. how often observers re-fixate previously fixated image positions 3.
  • scanapath_RQA_determinism(): Given a recurrence plot computed from a single scanpath, derives the percentage of recurrence points that form diagonal lines in the recurrence plot 3.
  • scanapath_RQA_laminarity(): Given a recurrence plot computed from a single scanpath, derives the percentage of entries from the upper half recurrence plot forming vertical and horizontal lines, which quantifies how often specific areas of a scene are repeatedly fixated 3.
  • scanapath_RQA_CORM(): Given a recurrence plot computed from a single scanpath, derives the distance of the center of gravity of recurrent points from the diagonal of self-recurrence—the main diagonal of the recurrence plot 3.
  • scanapath_RQA_entropy(): Given a recurrence plot computed from a single scanpath, derives the Shannon entropy of the distribution of diagonal line lengths, providing an estimate of the complexity within the scanpath's deterministic structure 53.

Scanpath comparison methods#

Scanpath direct comparison methods

  • scanpath_mannan_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the weighted mean distance between each fixation in one scanpath and its nearest neighbor (point mapping) in the other scanpath 62.
  • scanpath_eye_analysis_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the sum of all the point-mapping distances—from one sequence to the other and conversely—normalized by the number of points in the largest sequence 64.
  • scanpath_TDE_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the time delay embedding distance 93.
  • scanpath_DTW_distance(): Given a list of scanpaths, this metric seeks, for each pair of scanpaths, the temporal alignment that minimizes Euclidean distance between aligned scanpath fixations 8.
  • scanpath_frechet_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the minimum of the maximum distances between two scanpaths when they are continuously aligned, preserving their sequential order 23.

Scanpath string edit distance methods

For the following metrics, scanpaths are first spatially—and, if desired, temporally—binarized to generate a sequence of characters.

  • scanpath_levenshtein_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the minimum number of single-character edits (insertions, deletions, or substitutions) needed to transform one sequence into another. Computed using the Wagner–Fischer algorithm 92.
  • scanpath_generalized_edit_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the minimum number of single-character edits needed to transform one sequence into another. Also computed using the Wagner–Fischer algorithm 92, but allowing for distinct deletion and insertion costs, as well as a substitution cost based on the distance between spatial bins in the visual field.
  • scanpath_needleman_wunsch_distance(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the optimal alignment between two sequences through substitutions and gap insertions. While the Wagner–Fischer algorithm works with penalties for divergent segments, the Needleman–Wunsch approach introduces matching bonuses between pairs of segments, allowing negative matches only when the segments are very different 69.

Scanpath saliency comparison methods between a reference saliency map and an observer scanpath

  • scanpath_NSS(): Given a scanpath and a reference saliency map, computes the normalized scanpath saliency metric by first normalizing the saliency map. This produces a z-score which shows how many standard deviations a particular fixation location is above chance. Finally, the NSS value for a given fixation location is computed on a small neighborhood centered on that location.
  • scanpath_percentile(): Given a scanpath and a reference saliency map, quantifies similarity by calculating the average percentile rank of each fixation's saliency value 74.
  • scanpath_ROC(): Given a scanpath and a reference saliency map, leverages the Area Under the ROC Curve (AUC) measure to assess how well a reference saliency map predicts fixations by treating it as a binary classifier across varying thresholds 12.
  • scanpath_information_gain(): Given a scanpath and a reference saliency map, measures the extent to which a saliency model predicts recorded fixations compared to a center prior baseline 52.

Scanpath saliency comparison methods between a pair of scanpaths

  • scanpath_pearson(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the Pearson correlation coefficient as the linear relationship between two saliency maps 56.
  • scanpath_KL(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the Kullback–Leibler divergence which measures the information loss when the input saliency map approximates the reference, with lower scores indicating a closer match 55.
  • scanpath_EMD(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, spatial differences between two distributions by measuring the minimum cost to morph one into the other 81.

Scanpath cross-recurrence quantification analysis

  • scanapath_CRQA_recurrence_rate(): Given a list of scanpaths, a cross-recurrence matrix is first computed from each pair of scanpaths. From each matrix, cross recurrence rate is derived as the percentage of fixations that match between the two fixation sequences 63.
  • scanapath_CRQA_determinism(): Given a list of scanpaths, a cross-recurrence matrix is first computed from each pair of scanpaths. From each matrix, cross determinism is derived as the percentage of cross-recurrent points that form diagonal lines—representing fixation trajectories common to both fixation sequences 63.
  • scanapath_CRQA_laminarity(): Given a list of scanpaths, a cross-recurrence matrix is first computed from each pair of scanpaths. From each matrix, cross laminarity is derived as the percentage of consecutive recurrence points in one fixation series that are aligned vertically with recurrence points in the other series, forming vertical structures in the combined recurrence plot 63.
  • scanapath_CRQA_entropy(): Given a list of scanpaths, a cross-recurrence matrix is first computed from each pair of scanpaths. From each matrix, cross entropy estimates the complexity of the attunement between the two scanpaths under study 63.

Scanpath specific similarity metrics

  • scanpath_subsmatch_similarity(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the Subsmatch similarity 50. The method first converts scanpaths into character strings by spatially binning fixation sequences, then counting the number of occurrences of all subsequences of size n in each scanpath. Subsequently, the difference in occurrence frequency is used as the basis to evaluate similarity or dissimilarity between pairs of scanpaths.
  • scanpath_scanmatch_score(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the ScanMatch score 18. This method begins by converting scanpaths into character strings through spatial and temporal binning of fixation sequences. The resulting character sequences are then compared by maximizing a similarity score computed using the Needleman–Wunsch algorithm. The core of the ScanMatch approach is in its construction of a similarity matrix for regions within the visual field: a threshold is applied, making substitution matrix values positive for closely related regions and negative for regions with weaker relationships.
  • scanpath_multimatch_alignment(): Given a list of scanpaths, this metric computes, for each pair of scanpaths, the MultiMatch alignment algorithm 21, a vector-based, multi-dimensional method for assessing scanpath similarity. In this approach, vectorized and simplified scanpaths are compared, allowing for a comprehensive multidimensional similarity assessment.

Areas of interest#

A concise summary of the metrics and methods included in the VisionToolkit library for characterizing AoI sequences. Each metric is accompanied by a reference to the source article that guided its implementation.

AoI identification#

AoI identification methods available:

  • I_AP: Performs AoI identification using an affinity propagation algorithm which identifies exemplars—representative fixation points for each AoI—by iteratively passing messages between data points based on their similarity 28.
  • I_DP: Performs AoI identification using density peak clustering, which considers two properties of fixation points, namely local density (computed as the number of fixation points within a user-defined distance) and distance from points with higher density 57.
  • I_DT: Performs AoI identification using the DBSCAN clustering method, which detects areas of high density separated by low-density regions 26.
  • I_KM: Performs AoI identification using a K-means clustering method 76.
  • I_MS: Performs AoI identification using mean shift clustering which iteratively shifts data points toward the densest region in feature space, then applies a distance threshold to separate them into clusters 85.

AoI Markov-based analysis#

  • AoI_transition_matrix(): Given an AoI sequence, computes transition probabilities between visual elements, represented as a transition matrix 39.
  • AoI_transition_entropy(): Given an AoI sequence, computes transition probabilities between visual elements, represented as a transition matrix. Then, from the inferred transition matrix, the following entropies are computed: stationary entropy, joint entropy, conditional entropy and mutual information 49.
  • AoI_HMM(): Given a fixation sequence, learns parameters of a Hidden Markov Model using a Baum–Welch algorithm 9.
  • AoI_HMM_transition_entropy(): Given a fixation sequence, learns parameters of a Hidden Markov Model using a Baum–Welch algorithm. Then, from the inferred transition matrix, the following entropies are computed: stationary entropy, joint entropy, conditional entropy and mutual information 49.
  • AoI_HMM_fisher_vector(): Given a fixation sequence, learns parameters of a Hidden Markov Model and the corresponding Fisher vector 42. The idea of a Fisher kernel is to compute how a new sequence of gaze data would change the parameters of the model—i.e. the parameter gradients of the generative model when given a novel time series as input.

AoI pattern mining#

Pattern mining methods available:

  • AoI_lempel_ziv(): Given an AoI sequence, quantifies the complexity of visual scanning paths 60. The AoI sequence is scanned from left to right in order to identify new elements or sets of elements which have not yet been identified, then stored in a codebook. The complexity of Lempel–Ziv is a numerical value computed by considering the number of different patterns recorded in the codebook.
  • AoI_ngram(): Given an AoI sequence, assesses the distribution of fixed-length subsequences within gaze data. The possible n-grams with a given alphabet are calculated using combinatorics, and their occurrence in the AoI sequence counted. Subsequently, their frequencies and distributions are derived 51.
  • AoI_t_patterns(): Given an AoI sequence, identifies statistically recurrent temporal patterns in visual behaviors, with tolerance for gaps 83.
  • AoI_SPAM(): Given a list of AoI sequences, computes the Sequential Pattern Mining algorithm which finds frequent sequences or patterns in a dataset. It combines depth-first search with efficient bitwise operations to track sequence occurrences 5.

AoI sequence global alignment#

Alignment methods available:

  • AoI_levenshtein_distance(): Given a list of AoI sequences, this metric computes, for each pair of AoI sequences, the minimum number of single-character edits (insertions, deletions, or substitutions) needed to transform one AoI sequence into another. Computed using the Wagner–Fischer algorithm 92.
  • AoI_generalized_edit_distance(): Given a list of AoI sequences, this metric computes, for each pair of AoI sequences, the minimum number of single-character edits needed to transform one AoI sequence into another. Also computed using the Wagner–Fischer algorithm 92, but allowing for distinct deletion and insertion costs, as well as a substitution cost based on the distance between spatial bins in the visual field.
  • AoI_needleman_wunsch_distance(): Given a list of AoI sequences, this metric computes, for each pair of AoI sequences, the optimal alignment between two AoI sequences through substitutions and gap insertions. While the Wagner–Fischer algorithm works with penalties for divergent segments, the Needleman–Wunsch approach introduces matching bonuses between pairs of segments, allowing negative matches only when the segments are very different 69.

AoI common subsequence#

Available methods to assess common subsequences:

  • AoI_longest_common_subsequence(): Given a list of AoI sequences, this metric identifies, for each pair of AoI sequences, the longest subsequence common to two sequences by using dynamic programming.
  • AoI_smith_waterman(): Given a list of AoI sequences, this metric identifies, for each pair of AoI sequences, similar patterns among observer AoI sequences using a dynamic programming approach that incorporates a gap penalty function and a substitution matrix. This matrix is based on the distances between AoIs and employs a threshold value for scoring matches and mismatches 97.
  • AoI_eMine(): Given a list of AoI sequences, it first chooses the two most similar sequences according to the Levenshtein distance, before applying the longest common subsequence technique to these two scanpaths to find their common scanpath. Subsequently, the two selected sequences are removed from the input set and replaced by their longest common sequence. The process is repeated until there is a single sequence remaining, providing a common AoI sequence 24.
  • AoI_trend_analysis(): Given a list of AoI sequences, the scanpath trend analysis algorithm first analyzes the most-visited visual elements, groups the subsequences by organizing these visual elements according to their overall position in the individual sequences, and finally builds a trend sequence based on these visual elements 25.
  • AoI_CDBA(): Given a list of AoI sequences, the candidate-constrained dynamic time warping barycenter averaging iteratively aggregates multiple sequences into a single one by computing the barycenter of the experimentally recorded sequences 58.
  • AoI_hierarchical_clustering(): Given a list of AoI sequences, produces the hierarchical clustering from the distance matrix provided by the Smith–Waterman pair distances between input sequences 97.
  • AoI_dotplot_clustering(): Given a list of AoI sequences, produces the hierarchical clustering from the distance matrix computed through a two-step procedure 31.

AoI visualization tools#

  • AoI_time_plot(): Given an AoI sequence, returns a time plot which displays discrete AoIs on the vertical axis, while time is indicated on the horizontal axis 78.
  • AoI_scarf_plot(): Given a list of AoI sequences, plots a scarf diagram—a visualization tool designed to compare AoI sequences across different observers. The diagram represents various areas of interest along the vertical axis and time progression along the horizontal axis. Each AoI is assigned a unique color, with a separate time bar displayed for each observer, facilitating visual comparison of their gaze patterns over time 10.
  • AoI_sankey_diagram(): Given a list of AoI sequences, plots a Sankey diagram, a convenient visualization method for investigating time-varying fixation frequencies together with transitions between areas of interest obtained from a large number of input AoI sequences 10.
  • AoI_directed_graph(): Given an AoI sequence and its transition matrix, plots a directed graph which shows the transitions between AoIs, with each node representing an area of interest, while links describe the transitions 10.
  • AoI_chord_diagram(): Given an AoI sequence and its transition matrix, plots a chord diagram, a popular high-dimensional visualization tool for representing connections between nodes 95. Their simplicity and intuitive design—a radial layout allows all nodes to be directly connected to all other nodes—results in common use for affiliation visualization.
  • AoI_hierarchical_flow(): Given an AoI sequence and its transition matrix, plots a flow diagram where the different AoIs represent vertices of a graph and are visualized as rectangular boxes. These boxes are organized in vertically stacked layers, depending on their average order in the AoI sequence 11.

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