An High-Order Graph Generating Neural Network

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 (usually unsupervised). These network models can be used as neighborhood preserving map and some of them generate a perfect topology preserving map of the input manifold using competitive Hebbian rule. But such a structure is difficult to manage if it lays in a high-dimensional space and some hierarchical algorithms were proposed in order to obtain an 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 hierarchical structures 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 perfect topology preserving map if is trained using a graph that is also a topology preserving map.