SOM

Properties of the Feature Map

1. Approximation of the input space: The feature map $\Phi$ represented by a set of synaptic weight vectors $\mathbf{w}_j$ in the output space $\mathscr{A}$ provides a good approximation to the input space $\mathscr{H}$
2. Topological ordering: The feature map $\Phi$ computed by the SOM algorithm is topologically ordered in the sense that the spatial location of a neuron in the lattice corresponds to a particular domain or feature of input neurons.
3. Density matching: The feature map $\Phi$ reflects variations in the statistics of the input distribution: regionms in the input space $\mathscr{H}$ from which sample vectors $\mathbf{x}$ are drawn with a high probability of occurance are mapped onto larger domains of the output space $\mathscr{A}$ and therefore with better resolution than regions in $\mathscr{H}$ from which sample vectors are drawn with a low probability of occurance.
4. Feature selection: Given data from an input space with a non linear distribution the SOM is able to select a set of best features for approximating the underlying distribution