Topology conserving mappings for learning motor tasks

The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem

In this paper we introduce a new self-organizing neural network, the Kohonen Network Incorporating Explicit Statistics (KNIES) that is based on Kohonen's Self-Organizing Map (SOM). The primary difference between the SOM and the KNIES is the fact that every iteration in the training phase includes two distinct modules-the attracting module and the dispersing module. As a result of the newly introduced dispersing module the neurons maintain the overall statistical properties of the data points. Thus, although in SOM the neurons individually find their places both statistically and topologically, in KNIES they collectively maintain their mean to be the mean of the data points, which they represent. Although the scheme as it is currently implemented maintains the mean as its invariant, the scheme can easily be generalized to maintain higher order central moments as invariants. The new scheme has been used to solve the Euclidean Travelling Salesman Problem (TSP). Experimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSPLIB-A travelling salesman problem library. ORSA Journal on Computing, 3, pp. 376-384] indicate that it is a very accurate NN strategy for the TSP-probably the most accurate neural solutions available in the literature.

Self-organization of firing activities in monkey's motor cortex: trajectory computation from spike signals

The population vector method has been developed to combine the simultaneous direction-related activities of a population of motor cortical neurons to predict the trajectory of the arm movement. In this article, we consider a self-organizing model of a neural representation of the arm trajectory based on neuronal discharge rates. As self-organizing feature map (SOFM) is used to select the optimal set of weights in the model to determine the contribution of an individual neuron to an overall movement representation. The correspondence between movement directions and discharge patterns of the motor cortical neurons is established in the output map. The topology-preserving property of the SOFM is used to analyze the recorded data of a behaving monkey. The data used in this analysis were taken while the monkey was tracing spirals and doing center-->out movements. The arm trajectory could be well predicted using such a statistical model based on the motor cortex neuronal firing information. The SOFM method is compared with the population vector method, which extracts information related to trajectory by assuming that each cell has a fixed preferred direction during the task. This implies that these cells are acting along lines labeled only for direction. However, extradirectional information is carried in these cell responses. The SOFM has the capability of extracting not only direction-related information but also other parameters that are consistently represented in the activity of the recorded population of cells.

Adaptive, associative, and self-organizing functions in neural computing

This paper contains an attempt to describe certain adaptive and cooperative functions encountered in neural networks. The approach is a compromise between biological accuracy and mathematical clarity. two types of differential equation seem to describe the basic effects underlying the information of these functions: the equation for the electrical activity of the neuron and the adaptation equation that describes changes in its input connectivities. Various phenomena and operations are derivable from them: clustering of activity in a laterally interconnected nework; adaptive formation of feature detectors; the autoassociative memory function; and self-organized formation of ordered sensory maps. The discussion tends to reason what functions are readily amenable to analytical modeling and which phenomena seem to ensue from the more complex interactions that take place in the brain.