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Taylor Hayes, Per Sederberg, Alexander Petrov; A new technique for the analysis of sequential eye movements. Journal of Vision 2011;11(11):501. doi: 10.1167/11.11.501.
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© 2017 Association for Research in Vision and Ophthalmology.
Eye movement patterns contain important information about the underlying perceptual and cognitive mechanisms. Traditional area of interest (AOI) measures such as fixation count, fixation duration, scan-path length, and spatial density ignore either the spatial or the temporal aspects of fixation sequences. The transition-probability matrix contains both spatial and sequential information, but it only quantifies pairs of transitions and ignores properties of temporally-extended sequences. Here we describe a new method that captures the statistical regularities in longer sequences using successor representations (SRs, Dayan, 1993, Neural Computation). Whereas, each cell of a traditional transition matrix represents the frequency of making a single saccade from one AOI to another, the SR uses temporal difference learning to incrementally strengthen the weights of multiple cells based on both recent and predicted future transitions. The result is a matrix representation that integrates over multiple time steps to estimate the expected discounted number of future fixations at location j given a current fixation at location i. This new method was applied to eye movement data from 35 participants that solved items from Raven's Advanced Progressive Matrices test (APM). We performed a principal component analysis on the SRs for each individual participant and used the components to predict the individual APM scores. The two components with highest regression weights had a clear and intuitive interpretation: one captured the systematicity of scanning patterns and the other quantified the tendency to toggle to and from the response area. This supports the theory that high-scoring individuals use a constructive matching strategy and low-scoring individuals use a response elimination strategy. Leave-one-out cross validation demonstrated that these two components explained over 44% of the variance in APM scores, compared to 22% for a traditional transition matrix analysis. The SR technique thus shows great promise for analyzing temporally extended fixation sequences.
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