Error potentials for self-organization

An error potential for self-organizing learning rules is given. The gradient of this error potential leads to the well-known learning rule of Kohonen, except for the determination of the 'winning' unit. The existence of an error potential facilitates a global description of the learning process. A one-dimensional topological map is treated as an example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>