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Noah Benson, David Brainard; An Unsupervised Learning Technique for Typing Cones in the Retinal Mosaic. Journal of Vision 2012;12(9):110. doi: https://doi.org/10.1167/12.9.110.
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© ARVO (1962-2015); The Authors (2016-present)
Extracting color information from the interleaved retinal cone mosaic requires taking account of the spectral type (L, M or S) of each cone. Yet, there is no known biochemical mechanism that distinguishes L and M cones. We therefore ask whether unsupervised learning can distinguish the types of retinal cones. To investigate, we computed the responses of simulated cone mosaics to calibrated natural images. We considered mosaics with L:M cone ratio varying from 7:1 to 1:7, with the number of S cones held at ~7% of the total, and with random assignment of the locations of L and M cones. To learn cone types, our algorithm first found the correlation matrix of the responses of all of the cones in the mosaic. It then treated the correlation between any pair of cones as a measure of that pair’s similarity and applied non-metric multidimensional scaling to embed each cone at a location in a three-dimensional space, such that the distance between any pair of cones was monotonically related to that pair’s similarities. Density clustering was applied to the three-dimensional representation to find the best three-cluster representation. These clusters correctly grouped together cones of each type for all of our simulated mosaics, based on responses to ~5000 natural images: cone types can be learned without the need for biochemical identification. The feature of natural images and cone spectral sensitivities that supports unsupervised learning via our algorithm is that highly correlated cone pairs are highly likely to be of the same type, as long as the maximum retinal distance between cones of the same type is not too large. Further calculations should allow us to elucidate boundary conditions (e.g., separation of L and M lambda-max, L:M cone ratio) on when unsupervised learning is possible, and thus inform theories of how color vision evolved.
Meeting abstract presented at VSS 2012
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