A Novel Approach to Measure the Topology Preservation of Feature Maps

Abstract

Kohonen’s self-organizing feature map (SOFM) (Kohonen 1984) creates a topology preserving map from a data manifold M ⊆ V onto a lattice A of neural units i. The topology preserving property can be employed in a variety of information processing tasks, ranging from classification over robotics to data reduction and knowledge processing. To each neural unit i of A a reference or synaptic weight vector wi is assigned, defining the receptive field or Voronoi polyhedron Vi of each unit i by the set of all data points v ∈ M which are matched best by this reference vector. This mapping from the data manifold M onto the lattice A is called topology preserving, if neighbouring units i have receptive fields Vi which are adjacent on M. Under certain conditions, i.e., if a topological mismatch between M and A exists, the lattice folds itself into V and the topology preservation may be lost (Ritter et al. 1992).