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Toshiro Kubota; Computational models for self-organization of retinal neurons in Euclidean space. Journal of Vision 2008;8(17):65. doi: 10.1167/8.17.65.
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© ARVO (1962-2015); The Authors (2016-present)
Biologically, there are at least two factors that influence the plasticity: 1) geometrical structures and wiring among dendrites and axons and 2) distributions of neuro-transmitters and other chemicals. The former is slow changing and may be vital to self-organization and learning. The latter is faster changing and may be vital to adaptation. The goal of our current study is to derive a computational model that embraces the two factors.
To map the biological motivation to computational terms, we assign to each neuron a family of smooth single valued functions controlled by a few parameters. The function models its synaptic efficacy distribution (ϕ). Based on a sequence of external stimuli, a neuron assigns to each neighbor neuron the value(s) of independent variable(s) at which ϕ is evaluated to derive the synaptic efficacy between the pair. We call this long-term plasticity. Based on the current network state, the neuron adjusts the parameters of ϕ to adjust the synaptic efficacy distribution. We call this short-term plasticity.
In our current work, we focus on the computational mechanism for the long-term plasticity. The goal is to assign each neuron an X–Y coordinate so that the distance in the two-dimensional space approximates the distance in the space of past stimuli. We can achieve the goal using the principle component analysis (PCA). A tricky part is to do the computation incrementally as the dimension of the stimulus space increases as a new stimulus arrives. We present an incremental PCA algorithm that can approximate the Euclidean distance computed by the PCA, and demonstrate its effectiveness with stimuli derived from patches of small natural images.
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