Self organizing map is claimed to be able to visualize/cluster the high-dimensional data on a smaller dimensional space. I have some difficulties in understanding this statement.
Consider a six-dimensional data set, the codebook vector/reference vector is also of six-dimensional. According to the SOM algorithm, updating these reference vectors are also conducted in the six-dimensional vector space. If we are considering a two dimensional map, how should I understand the map between the six-dimensional data space and two-dimensional map space?
The map between the N-dimensional input space and the 2D SOM space is a non-linear projection preserving as much of the topology as possible.
It means that information about distance and angle is lost in the process but that proximity relationship between points is preserved (i.e. 2 points which are close one to another in the input space should be close in the SOM space).
I got my best insight in “what does a SOM do?” by using it on the 3D RGB color space: the work of the SOM can easily be visualized in this case and should help to grasp the concept.