Kohonen Network

Definition

Combines both Hamming Network and MaxNet, in sequence, then brings the winner node closer to the input node.

Algorithm

  1. Initialize random weights and learning rate η\eta.
  2. Find the winning cluster jj (of mm clusters) which is the cluster closest to the input vector x=[x1xn]x=[x_{1}\ldots x_{n}] (minimize the squared distance of each cluster’s weight with respective element of vector) with each cluster’s associated weight wj,iw_{j,i} minj=1,..mD(j)=minj=1,..m{i=1n(xiwj,i)2}\min_{j=1,..m} D(j)=\min_{j=1,..m}\left\{\sum\limits_{i=1}^{n}(x_{i}-w_{j,i})^{2}\right\}
  3. Update each wj,iw_{j,i} for the chosen jj like so: Δwj,i=η(t)(xiwj,i), wj,i=wj,iΔwj,i\Delta w_{j,i}=\eta(t)(x_{i}-w_{j,i}), \ w_{j,i}=w_{j,i}-\Delta w_{j,i}for i{1,,n}i\in\{1,\ldots,n\}
  4. Repeat until network converges.