KOHOMAP: The Kohonen Self-organizing Map

Abstract

As discussed in Sect. 15.2.3 Kohonen’s topology-preserving map creates a representation of a multidimensional continuous “sensory space” on a grid of neurons. Here we will denote the sensory input by x = (x ₁, . . . , x _d ). This is assumed to be a d-dimensional vector with real-valued components, taking on values in a subspace V ∈ ℝ^d. Exemplars of such vectors are repeatedly presented to the network, simulating the varying stimuli experienced by a sensory organ. The values of x are drawn randomly according to a given probability distribution which may be nonuniform over the range of possible values V. The N = N _x × N _y neurons of the network are thought to be organized in a two-dimensional grid so that each neuron can be labeled by a vector n = (n _x , n _y ), where n _x , n _y are integer counting indices in the range 1 ≤ n _i ≤ N _i .