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I am doing some work which requires fitting a Gaussian to a cluster of points which is expected to be distributed normally.

I have data which looks like this, you can see the small tightly grouped cluster of points on the left:

enter image description here

I zoom in around the cluster, and use scikit-learn KDE to get a density distribution (with Gaussian kernel), which looks like this:

enter image description here

Then I fit the Gaussian and it turns out to have far too small sigma:

centroid_x: -36.3204357 
centroid_y: -12.8734763
sigma_x:     0.17916588
sigma_y:     0.07428976

enter image description here

From inspection of the density distribution, the x and y sigma should be more on the order of ~1, rather than ~0.1. Does anyone know why this behaviour might be occurring? I don't believe there are significant errors in my code or method, this technique has worked well on other data sets, for example:

enter image description here enter image description here enter image description here

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  • $\begingroup$ Are you isolating the points (i.e., does the data set you're fitting to consist of only the points visible in the second plot)? Do you set initial values? $\endgroup$
    – corey979
    Commented May 18, 2020 at 19:41
  • $\begingroup$ Hi! the fitting is only done with the points shown in the second plot. For initial values I use the mean and standard deviations of the x and y arrays $\endgroup$
    – big daddy
    Commented May 18, 2020 at 19:57
  • $\begingroup$ I am unconvinced there is anything the matter, because you haven't shown the points in sufficient detail. Your graphics and results are perfectly consistent, assuming there is a pile of very closely clustered points near $(-36.5, -13).$ What have you done to investigate this possibility? $\endgroup$
    – whuber ♦
    Commented May 18, 2020 at 20:28
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    $\begingroup$ Can you post the points you're fitting to, so that we could experiment? $\endgroup$
    – corey979
    Commented May 18, 2020 at 21:04

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