How does one visualize the self-organizing map of $n$-dimensional data

Question

I have a data set consisting from $7$-dimensional data points. I want to produce a self-organizing map for this data to see how my data is clustered.

I have been reading some tutorials from the internet about SOM and I usually see this classical example of training the SOM to learn colours (the image is cited from http://www.ai-junkie.com/ann/som/som1.html):

I'm a bit confused because I don't know how to produce an image similar to the example above when I have $7$-dimensional data. How is SOM usually visualized with $n$-dimensional data? What should I do specifically?

My question is a bit similar to this question: Self Organizing Maps: How is the location computed and updated?

Thank you for any clarifications!

P.S. I'm using Matlab in my analysis.

Answer 1

This is what I have done to see how the map fits the data

Wickham, H.; Cook, D. & Hofmann, H. (2015), 'Visualizing statistical models: Removing the blindfold.', Statistical Analysis and Data Mining 8 (4), 203-225 link

And there are videos at: ggobi book

Answer 2

One method I have had success with is to produce a 2D Sammon Map of the trained SOM node vectors. The positions of the nodes on the Sammon Map can then be projected onto a two-dimensional colour space. The distance between the nodes on the Sammon Map is approximately proportional to the distance between the nodes in the original $n$-dimensional data space. Nodes with similar $n$-D vectors will thus be assigned similar colours.