von der Malsburg and Vasishth Version 1

A Similarity Measure for Scanpaths Sensitive to Fixation Durations
and the Location of Fixation Targets

Titus von der Malsburg and Shravan Vasishth

In the investigation of reading, word-based measures such as first fixation
duration, gaze duration and regression probability, are commonly used for
analyzing the empirical data. However, these measures are not always adequate
when the effect of an experimental manipulation is expected to appear in the
patterns of fixations rather than in local measures, e.g. when reanalysis
strategies in temporarily ambiguous sentences are studied. We address this
shortcoming by proposing alternative methods for analyzing eye movements
that are based on the notion of similarity of scanpaths. For this
purpose we introduce a measure that quantifies the similarity of two scanpaths
with respect to their fixation patterns and their temporal dynamics.

Our metric is a member of the class of edit-distances of which the Levenshtein
metric is a well-known instance (Levenshtein 1968). Edit-distances have already
been used for analysing eye tracking data in a variety of studies outside
reading research, for example in experiments studying scene perception or the
usability of graphical user interfaces [citation]. While edit-distances capture
the topological similarities of scanpaths, they operate on a representation of
scanpaths that neglects properties that are crucial when studying reading. The
first is fixation duration, which is one of the most important and best studied
sources of evidence in online reading research. Secondly, the available
edit-distance measures are insensitive to the proximity of regions of interest.
However, the observation of parafoveal preview effects suggest that the spatial
relations of regions of interest do play an important role and should be
accounted for [cite something that demonstrates preview effects].

We addressed these deficits in standard edit-distance measures by replacing the
cost function of the Levenshtein metric. Our new cost function compares
fixations with respect to their duration and spatial distance. Thus, the way
distance is incorporated is motivated by findings about the distribution of
acuity in the visual field (cortical magnification, Rovamo, Virsu, N‰s‰nen,
1978). The resulting measure operates on a parsimonious representation of eye
movement data and can efficiently be computed (O(m*n), where n, m are the
numbers of fixations of the two compared scanpaths).

We suggest several approaches for analysing eye movement data based on this new
measure: 1.) Cluster analysis can be applied to scanpaths in order to identify
reading strategies among experimental conditions and among subjects. 2.) The
variance of the pairwise similarities in sets of scanpaths can be compared to
the variance of the union of those sets in order to determine whether they
represent different populations. 3.) String interpolation methods and
optimization techniques can be used for computing prototypical scanpaths for
sets of scanpaths.

Areas of investigation where these methods might also be useful comprise the
evaluation of models of oculo-motor control, classification of reading
disorders, analysis of cognitive strategies in experiments using the visual
world paradigm.

As opposed to approaches using word-based measures, the proposed similarity-based
methods enable the analysis of the full available data and do not necessitate
averaging of variables thereby preserving possibly crucial information. The
main benefit of our similarity measure is that it is sensitive to fixation
patterns and the temporal dynamics in a scanpaths at the same time.

References:

[coming soon]