A high-order graph generating self-organizing structure

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.