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Elements of an <t>HMM</t> fitted to an individual scanpath. ( A ) ROIs corresponding to three states (ellipses) and a modelled scanpath consisting of individual samples registered by an eye tracker (dots). ( B ) Transition matrix, determining the probabilities of transitioning between each two states. High values at the diagonal indicate that at any given time, staying in the same state (fixating the ROI) is more probable than moving to a different state (making a saccade). ( C ) Prior, determining for each state the probability that a sequence of states generated by the HMM starts from it. Note that this Figure presents a contrived illustration, not an HMM fitted to real data. HMM = hidden Markov model; ROI = region of interest.
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Elements of an HMM fitted to an individual scanpath. ( A ) ROIs corresponding to three states (ellipses) and a modelled scanpath consisting of individual samples registered by an eye tracker (dots). ( B ) Transition matrix, determining the probabilities of transitioning between each two states. High values at the diagonal indicate that at any given time, staying in the same state (fixating the ROI) is more probable than moving to a different state (making a saccade). ( C ) Prior, determining for each state the probability that a sequence of states generated by the HMM starts from it. Note that this Figure presents a contrived illustration, not an HMM fitted to real data. HMM = hidden Markov model; ROI = region of interest.

Journal: Journal of Vision

Article Title: Influence of prior knowledge on eye movements to scenes as revealed by hidden Markov models

doi: 10.1167/jov.23.10.10

Figure Lengend Snippet: Elements of an HMM fitted to an individual scanpath. ( A ) ROIs corresponding to three states (ellipses) and a modelled scanpath consisting of individual samples registered by an eye tracker (dots). ( B ) Transition matrix, determining the probabilities of transitioning between each two states. High values at the diagonal indicate that at any given time, staying in the same state (fixating the ROI) is more probable than moving to a different state (making a saccade). ( C ) Prior, determining for each state the probability that a sequence of states generated by the HMM starts from it. Note that this Figure presents a contrived illustration, not an HMM fitted to real data. HMM = hidden Markov model; ROI = region of interest.

Article Snippet: To model our scanpaths as HMMs, that is, find HMMs that were most likely to generate the scanpaths recorded on the critical frames, we used the SMAC with HMM toolbox ( ; see also ).

Techniques: Sequencing, Generated

Results from the different variants of the classification analysis. Dots on all panels represent individual critical frames. The results for HMMs before and after their dimensionality has been reduced by retaining only their first principal component are shown on, respectively, ( A and B ). Notice that the dimensionality reduction leads to lower chance levels and an increase in the percent of frames classified above chance. For details, see the section HMMs and classification: Caveat one—chance levels. ( C ) For each frame, the highest and the lowest classification accuracy obtained in 10 repetitions of the classification analysis, where each repetition was conducted on HMMs fitted after initializing the random number generator with a different seed (number). For details, see the section HMMs and classification: Caveat two—a random number generator. Note that the ordering of frames is different on each panel: on ( A and B ), they are ordered by the increasing obtained accuracy, whereas on ( C ) they are ordered by the increasing lowest accuracy. Red circles on all panels indicate results for the same critical frame. On the left-hand side of each panel, marginal density plots are presented. HMM = hidden Markov model.

Journal: Journal of Vision

Article Title: Influence of prior knowledge on eye movements to scenes as revealed by hidden Markov models

doi: 10.1167/jov.23.10.10

Figure Lengend Snippet: Results from the different variants of the classification analysis. Dots on all panels represent individual critical frames. The results for HMMs before and after their dimensionality has been reduced by retaining only their first principal component are shown on, respectively, ( A and B ). Notice that the dimensionality reduction leads to lower chance levels and an increase in the percent of frames classified above chance. For details, see the section HMMs and classification: Caveat one—chance levels. ( C ) For each frame, the highest and the lowest classification accuracy obtained in 10 repetitions of the classification analysis, where each repetition was conducted on HMMs fitted after initializing the random number generator with a different seed (number). For details, see the section HMMs and classification: Caveat two—a random number generator. Note that the ordering of frames is different on each panel: on ( A and B ), they are ordered by the increasing obtained accuracy, whereas on ( C ) they are ordered by the increasing lowest accuracy. Red circles on all panels indicate results for the same critical frame. On the left-hand side of each panel, marginal density plots are presented. HMM = hidden Markov model.

Article Snippet: To model our scanpaths as HMMs, that is, find HMMs that were most likely to generate the scanpaths recorded on the critical frames, we used the SMAC with HMM toolbox ( ; see also ).

Techniques:

Results of the classification analysis with dimensionality reduction conducted on the 10 sets of HMMs fitted to the same scanpaths but differing regarding the seed of a random number generator used in the fitting procedure. IQR = interquartile range; SD = standard deviation. Each p < 0.05 is printed in bold.

Journal: Journal of Vision

Article Title: Influence of prior knowledge on eye movements to scenes as revealed by hidden Markov models

doi: 10.1167/jov.23.10.10

Figure Lengend Snippet: Results of the classification analysis with dimensionality reduction conducted on the 10 sets of HMMs fitted to the same scanpaths but differing regarding the seed of a random number generator used in the fitting procedure. IQR = interquartile range; SD = standard deviation. Each p < 0.05 is printed in bold.

Article Snippet: To model our scanpaths as HMMs, that is, find HMMs that were most likely to generate the scanpaths recorded on the critical frames, we used the SMAC with HMM toolbox ( ; see also ).

Techniques: Standard Deviation

Absolute values of loadings of HMM coefficients in the first principal components. Each boxplot shows the distribution of these values across all critical frames. Colors (see plot legend) encode elements of HMMs to which different coefficients (labelled on the x -axis and explained in the text) belong. Note that here, unlike in , we treat the centers of ROIs (states) and their covariance matrices as separate elements of HMMs and indicate them with different colors. HMM = hidden Markov model; ROI = region of interest.

Journal: Journal of Vision

Article Title: Influence of prior knowledge on eye movements to scenes as revealed by hidden Markov models

doi: 10.1167/jov.23.10.10

Figure Lengend Snippet: Absolute values of loadings of HMM coefficients in the first principal components. Each boxplot shows the distribution of these values across all critical frames. Colors (see plot legend) encode elements of HMMs to which different coefficients (labelled on the x -axis and explained in the text) belong. Note that here, unlike in , we treat the centers of ROIs (states) and their covariance matrices as separate elements of HMMs and indicate them with different colors. HMM = hidden Markov model; ROI = region of interest.

Article Snippet: To model our scanpaths as HMMs, that is, find HMMs that were most likely to generate the scanpaths recorded on the critical frames, we used the SMAC with HMM toolbox ( ; see also ).

Techniques: