Competitive Hebbian Learning Rule Forms Perfectly Topology Preserving Maps

摘要: The problem of forming perfectly topology preserving maps feature manifolds is studied. First, through introducing “masked Voronoi polyhedra” as a geometrical construct for determining neighborhood on manifolds, rigorous definition the term “topology map” given. Starting from this definition, it shown that network G neural units i, i = 1, …, N has to have lateral connectivity structure A, Aij ∈ {0, 1}, j 1,…, which corresponds “induced Delaunay triangulation” synaptic weight vectors wi ℜDin order form map given manifold M ⊆ ℜD features v M. connections determine relations between in network, match manifold. If all are distributed over M, and if distribution resolves shape can be Hebbian learning with competition leads —j (Aij 1) correspond edges and, hence, forms independent M’s topology. This yields means constructing arbitrarily structured manifolds.