Quantitative measures for the Self-Organizing Topographic Maps

Self-organizing topographic maps have found many applications as systems capable of unsupervised learning. They are based on the competitive learning algorithm applied to lowdimensional (in practice one, two or three-dimensional) structure of artificial neurons. The iterative algorithm used for competitive learning converges slowly and is computationally very intensive. In this paper direct mapping on the continuos space based on the minimization principle is used to map the high-dimensional input data to the low-dimensional target space. The problem of finding the best low-dimensional representation of the data is reduced to a minimization problem or to the solution of a system of nonlinear algebraic equations.