The Architecture

A Self-Organizing Map consists of an array of i, $1 \leq i \leq q$nodes connected to each other following some topology, e.g. linearly for the one-dimensional or in some form of grid for the two-dimensional case etc., forming the output layer. These interconnections, however, only define the neighborhood-relation between the nodes and have no weights assigned to them. Thus they do not directly influence the learning-process as opposed to other types of networks. The choice of a particular map-topology as well as the size of the map is application dependent. In most cases rectangular planes are chosen since they allow easy representation of the trained maps.

Each of the nodes forms an output-unit by having a weight vector m_i of the same dimension as the input space: $m_{i}=(\mu_{i_{1}}, \mu_{i_{2}},..,\mu_{i_{n}}), 1 \leq i \leq q, m_{i}\in \Re ^{n}$ assigned to it, defining its location in input space. These weight vectors are usually initialized with