Linear manifold topographic map formation based on an energy function with on-line adaptation rules

The lack of an energy function is an important problem in many topographic map formation methods. This paper describes formation of a map, called linear manifold topographic map, based on minimization of an energy function. Using multiple low-dimensional linear manifolds as data representation elements, the data distributions of many problems with high-dimensional data spaces can be simply and parsimoniously modeled. Two sets of on-line adaptation rules are obtained based on stochastic gradient descent on the energy functions devised for a soft and a hard data assignment. Experimental results show good performance of the map in comparison to other relevant techniques.