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Red Cloud

Take some time to look at the picture above. We can notice a red cloud. There's a red dense cloud and some irrelevant red points around that red cloud.

Suppose the red cloud to be the set of vector $V = \{v_1, v_2, ..., v_n\} \subset \mathbb{R}^3$. How can I get the dense cloud from $V$? In other words, how can I get rid of the irrelevant points around the dense red cloud?

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closed as unclear what you're asking by whuber Dec 10 '18 at 15:27

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ How are we to determine the "irrelevant" red points? Could you explain what you mean by "irrelevant"? And could you explain why you are also showing us green points, even though the question as stated seems to have nothing to do with them? Is it possible you are asking about multivariate outlier detection? $\endgroup$ – whuber Dec 10 '18 at 15:26
  • $\begingroup$ Just a small note, I am RG colourblind, so all those dots are the same colour to me. Can you switch to a different color palette? $\endgroup$ – Demetri Pananos Dec 10 '18 at 15:27
  • $\begingroup$ @DemetriPananos Suppose the points are the same color. That doesn't change the question. There are a lots of points out the main cloud. I just need to remove them. $\endgroup$ – davegaut Dec 10 '18 at 15:32
  • $\begingroup$ @whuber It is hard to explain an accurate definition for "irrelevant". We can look at the cloud with only one color instead of two as you can currently see on the picture. It is quite straightforward to see that there's a main cloud and some dirty points around it. All I want is to remove those points around the main cloud. $\endgroup$ – davegaut Dec 10 '18 at 15:39
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    $\begingroup$ That sounds like a qualitative description of "outlier." We'll have to take it as such unless you can provide some description to differentiate your concept from the ones embodied in the links I provided. $\endgroup$ – whuber Dec 10 '18 at 15:52
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Are you sure these are "irrelevant"? It looks like the underlying distribution could be Gaussian, and then these "irrelevant" points would just be points with a small probability but by random sampling (many) points from your distribution you would always get points like this.

If you really want to exclude them, you could calculate the distance to the "center" of the mass (mean) and then exclude all points for which the distance to the center is larger than a threshold.

Or you could fit a (multidimensional) Gaussian and exclude all points outside some percentile.

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