The Structure and Purpose

Competitive learning network is a typical unsupervised learning network composed of 2 layers: the input layer and the output layer containing $n$ and $m$ nodes, respectively.

When presented with an input pattern $X=[x_1,\cdots,x_n]^T$, the output nodes compete with each other in the following winner-take-all manner:

if $W_k^TX=max_i\{W_i^TX\;\;\;\;(i=1,\cdots,m)$

then $y_k=1$, else $y_k=0$.

where $W_i=[w_{i1},\cdots,w_{in}]^T$ is an n-D weight vector composed of all $n$ weights of the node to the input nodes. The output pattern can also be represented as an m-D vector $Y=[y_1,\cdots,y_m]^T$.

Given a large number of patterns $\{ X_i,\;\;(i=1,\cdots,N) \}$, the network will iteratively modify its weights through an unsupervised learning process to eventually reach a stable state so that a certain output node will be 1 while all others are 0 when any of a cluster of patterns is presented to the input layer. Competitive learning is very similar to the statistical clustering analysis methods (i.e., k-means method, ISODATA method), in the sense that each cluster of similar patterns is recognized and responded to.