# Can Gaussian Mixture Model Clustering tell me something about the distribution of my data?

I have 10,000 vectors originating from 5 separate classes (2,000 each). I use Gaussian Mixture Model clustering (in Python) to cluster the 10,000 vectors, telling the algorithm to cluster the data into 5 clusters:

gmm = GaussianMixture(n_components=5, covariance_type='full',random_state=0)


Then I find out the predicted cluster allocation of each vector and compare with the original classes:

y_pred = gmm.fit_predict(data)
etc.


I get very high accuracy (>98%), which means the algorithm is successfully able to cluster the data into its original classes.

Now I'm wondering whether this allows me to conclude anything about the distribution of my data. Since the GMM uses a mixture of 5 gaussians to cluster the data, does this mean I can assume:

1. each of my 5 classes is approximately gaussian?
2. the distribution of the 10,000 vectors is well represented by a mixture of 5 gaussians (the means/covariances of the gaussians being the cluster means/covariances that the GMM calculates)?

Why (not)?

I've tried a series of tests for normality on the individual classes (Anderson–Darling, Mardia’s test for multivariate normality, etc.) and these indicate that the individual classes are NOT normally distributed.

Can somebody explain how it's possible for a model that uses a mixture of gaussians to fit my data so well, but that it doesn't seem to imply much about the distribution of my data. Am I missing something obvious?