Learning in competitive networks with penalties

Modeling and approximation of functions by penalized competitive learning networks are described. The learning is based on winner-take-all or winner-take-quota. Cost functions are combinations of terms representing the data fitness and the qualification on the approximation. The sub-cost to confine the approximation is called competition handicap, constraint or penalty. Both additive and multiplicative penalties are allowed. Thus, the problem has relations to penalized learning and weight elimination. However, unsupervised learning or self-organization is of main interest here. A general learning equation based upon gradient descent is given. Important special cases such as combinatorial optimization, clustering and data transformation are individually discussed