This sounds very mathematical and complicated, so it will be helpful to look at a practical example and explore how those algorithms work. On a computer, colors are usually described by their amounts of red, green, and blue. Thus all colors construct a three-dimensional feature space, and a three-dimensional vector can describe each color. E.g. a SOM can be trained which sorts different colors using this [to do] interactive online demo.

A suitable training set has to be chosen at first by randomly selecting colors with the buttons on the upper right, then the Kohonen map will be shown. Each node of the map initially points to a random location in the feature space; in other words, a random color is assigned to each square of the map. To train the map we identify the nodes whose pointers are most proximate to the location of each item. So we sort our training data to the squares with the best matching colors.