I have a set of unlabeled data $x \in \mathbb R^n$, and I want to visualize how scattered those points are using python. In dimension 2, we can just use plt.scatter which is quite straightforward. I wonder whether there is any approach to deal with this in higher dimensions.
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1$\begingroup$ What properties of the result interest you? Clearly a monitor can't display data in more than 2 dimensions, so we will, in some way, be forced to make a compromise. Do you wish for the result to be orthogonal? Or preserve pairwise distances? Or something else? $\endgroup$– Sycorax ♦Commented Jul 24, 2020 at 18:39
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$\begingroup$ I am hoping to visualize whether all the points are sufficiently close to a given fixed point with respect to the Euclidean distances. A good indicator apparently is to directly calculate the average Euclidean distance. However, I do not quite have a good feeling about what the scale should be. So I wonder whether it is possible to have some sort of visualization. $\endgroup$– AdamCommented Jul 24, 2020 at 18:46
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1$\begingroup$ What, then, do you mean by "sufficiently" close? That might help answer the question. $\endgroup$– whuber ♦Commented Jul 24, 2020 at 19:04
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$\begingroup$ I am not sure about what threshold to pick, and that is exactly why I need to visualize a bit. $\endgroup$– AdamCommented Jul 24, 2020 at 19:06
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3$\begingroup$ Hm. If your main interest is the Euclidean distance from a given point, then a simple histogram of these distances may be a good start. Alternatively, you may want to look into multidimensional scaling, which attempts to project your points into two dimensions while preserving distances as much as possible. $\endgroup$– Stephan KolassaCommented Jul 24, 2020 at 21:08
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