# Dimensionality Reduction of Self Organising Maps

I've probably read any article on dimensionality reduction of Self Organising Maps but just couldn't fully comprehend this process.

My understanding so far is:

SOM are two-layer networks, whose layers (first - input layer, second - output layer) are connected via a weight matrix.

Dimensionality reduction is the process of reducing the dimensionality of input data to a lower (e.g. one or two) dimensionality, which will later be displayed by the Kohonen network (output layer).

Now the tough part begins..

Let's imagine we do have a 3 x 3 grid (9 points) and we want to represent the color space (3 dimension: red, green, blue).

What does happen next?

• (1) Does dimensionality reduction mean that the weight vectors which are assigned to any node in the output layer can be less then the dimensionality of the input samples?

or

• (2) Does dimensionality reduction only means that the high dimensionality of the sample data is reduced to the dimensionality of the output layer (in our case 2 dimensions - because of 3 x 3). However, any neuron of the output layer carries a weight vector whose dimensionality equals the dimensionality of the sample data?

To project that on our example

• To (1) - Our 3D-input space (red, green, blue) is reduced to (red, green).
• To (2) - Our 3D-input space is mapped onto a 2D-map, where any of the 9 nodes is carrying a vector which represents (red, green, blue)

I really hope that my explanation is comprehensive and you get my problem.
Thank you a lot!