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Math Help - How to visualize a GMM of more-than-3-dimensional data?

  1. #1
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    How to visualize a GMM of more-than-3-dimensional data?

    Hello!

    I was wondering if anyone has any hints about how to visualize a Gaussian Mixture Model (GMM) of data that has more than 3 dimensions?

    I know that a common method for visualizing high dimensional data is multidimensional scaling (MDS). What I'd like to do is to plot the data for which the GMM is computed by using MDS and visualize the means and covariances in the same plot. This can quite easily be done with the mean vectors, since they are single points and can just be added to the data set when MDS is applied. But I'm wondering how I could visualize the covariances?

    If anyone has any ideas, I'd be very happy.

    Thank you very much,
    Koffer
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  2. #2
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    Jan 2012
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    Re: How to visualize a GMM of more-than-3-dimensional data?

    Hi, Koffer

    Well, I don't know about MDS, but maybe one could use parallel coordinates to visualize the population data and then overlay the estimated means and covariances of the GMM. For each component of your GMM, visualizing the mean is trivial. For the covariances, you can at least mark the covariance range around the mean at the i-th dimension's axis with the according element from the diagonal of the covariance matrix. This method might already give you some idea about how well the GMM models your data. Of course this doesn't really show you the (i,j)-covariances for i != j, but I guess those could be explored too by interactively moving the i- and the j-axis of interest next to each other and range-marking the space in-between them by the according i,j-cov value.
    Haven't tried it (yet), and maybe there's some issue with this idea I didn't think of (if so, please correct me), but I think it's worth a shot.

    Cheers
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