I represent each RF using a multivariate Gaussian distribution with a mean vector (position), covariance matrix (alignment and size), and gain factor (response magnitude). I determine the value of each of these parameters for each RF using a competitive algorithm where the result of a custom greedy algorithm competes against the result of a genetic algorithm. Gaussians are trained one at a time in a staged approach so that the addition of each new Gaussian to the model takes into consideration the effects of all of the previously trained Gaussians.
Actually, the genetic algorithm applies a little more intelligence by dividing a population of Gaussians into species based on similar characteristics and mating (i.e. crossing-over) the best performing Gaussian members within the same species during each generation of evolutionary training. The addition of each new Gaussian to the model attempts to address some residual error in the model resulting from recorded neuron firing rate response values that have not yet been fully explained by the addition of previous Gaussian distributions. The theory is that the best performing Gaussian of each species is associated with a different local minima in the residual error search space, thereby increasing the chances that one of those Gaussians is associated with the global minimum. The Gaussian which results in the greatest drop in residual error among all of the species is selected and added to the model.
The Gaussian model (also known as a Scaled Gaussian Mixture Model) is then used to extract features that are fed into a linear regression (LR) technique. Why is LR necessary on top of the Gaussian model? The reason is because not all RFs are the same. A great deal of research indicates the existence of hotspot segments in the visual field which have a major impact on the response values generated by RFs in non-hotspot segments. Specifically, the directional preference of RFs associated with hotspot segments plays a major role. Thus, the response value of RFs associated with hotspot segment needs to be weighted differently than those for non-hotspot segments and the response values each segment needs to be divided into directional contribution vectors that are each weighted differently.
Overall my algorithmic approach trains models that are capable of predicting neuron firing rate response values with moderate to high accuracy. As such my research offers support for a number of existing concepts in the field of visual neuroscience, such as the gradient hypothesis and opponent organization.
Read the full report (PDF) for a complete explanation.
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