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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):

enter image description here

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.

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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

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    $\begingroup$ Thank you for your contributions here, @DiCook. Be aware that you now have two accounts new, original. Please merge your accounts (you can find information on how to do this in the My Account section of our help center). $\endgroup$ May 3, 2016 at 3:20
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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.

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