Self-organizing continuous attractor networks and path integration: one-dimensional models of head direction cells

Some neurons encode information about the orientation or position of an animal, and can maintain their response properties in the absence of visual input. Examples include head direction cells in rats and primates, place cells in rats and spatial view cells in primates. 'Continuous attractor' neural networks model these continuous physical spaces by using recurrent collateral connections between the neurons which reflect the distance between the neurons in the state space (e.g. head direction space) of the animal. These networks maintain a localized packet of neuronal activity representing the current state of the animal. We show how the synaptic connections in a one-dimensional continuous attractor network (of for example head direction cells) could be self-organized by associative learning. We also show how the activity packet could be moved from one location to another by idiothetic (self-motion) inputs, for example vestibular or proprioceptive, and how the synaptic connections could self-organize to implement this. The models described use 'trace' associative synaptic learning rules that utilize a form of temporal average of recent cell activity to associate the firing of rotation cells with the recent change in the representation of the head direction in the continuous attractor. We also show how a nonlinear neuronal activation function that could be implemented by NMDA receptors could contribute to the stability of the activity packet that represents the current state of the animal.     

Self-organizing continuous attractor networks and path integration: two-dimensional models of place cells

Single-neuron recording studies have demonstrated the existence of neurons in the hippocampus which appear to encode information about the place where a rat is located, and about the place at which a macaque is looking. We describe 'continuous attractor' neural network models of place cells with Gaussian spatial fields in which the recurrent collateral synaptic connections between the neurons reflect the distance between two places. The networks maintain a localized packet of neuronal activity that represents the place where the animal is located. We show for two related models how the representation of the two-dimensional space in the continuous attractor network of place cells could self-organize by modifying the synaptic connections between the neurons, and also how the place being represented can be updated by idiothetic (self-motion) signals in a neural implementation of path integration.     

Input variable selection: mutual information and linear mixing measures

Determining the most appropriate inputs to a model has a significant impact on the performance of the model and associated algorithms for classification, prediction, and data analysis. Previously, we proposed an algorithm ICAIVS which utilizes independent component analysis (ICA) as a preprocessing stage to overcome issues of dependencies between inputs, before the data being passed through to an input variable selection (IVS) stage. While we demonstrated previously with artificial data that ICA can prevent an overestimation of necessary input variables, we show here that mixing between input variables is common in real-world data sets so that ICA preprocessing is useful in practice. This experimental test is based on new measures introduced in this paper. Furthermore, we extend the implementation of our variable selection scheme to a statistical dependency test based on mutual information and test several algorithms on Gaussian and sub-Gaussian signals. Specifically, we propose a novel method of quantifying linear dependencies using ICA estimates of mixing matrices with a new linear mixing measure (LMM).     

Selecting inputs for modeling using normalized higher orderstatistics and independent component analysis

The problem of input variable selection is well known in the task of modeling real-world data. In this paper, we propose a novel model-free algorithm for input variable selection using independent component analysis and higher order cross statistics. Experimental results are given which indicate that the method is capable of giving reliable performance and that it outperforms other approaches when the inputs are dependent.