Self-organization in neural networks subject to random transformations

Transformations of the visual input, corresponding to eye movements and object motions, are of obvious importance in vision. This paper concerns the detection by prototype visual neural networks of the symmetry group structures which underlie such transformations. It is shown that a prototype network, with a simple Kohonen-type learning rule, self-organises in response to random transformations, to form an efficient and regular representation of the underlying symmetry groups. The convergence is irregular rather than smooth. Results are presented for networks with various combinations of rotation and (in 2D) dilation and translation. Some conclusions are drawn about the behaviour and possible applications of such networks and their relationship to other networks is briefly discussed.