VonMisesFisherMixture.log_likelihood() doesn't return a log likelihood value. What is it?

[mattroos]

I'd like to compute the AIC goodness of fit for a fitted model. This requires knowing the likelihood function value for the set of estimated vonMises-Fisher parameters. But what is being returned by VonMisesFisherMixture.log_likelihood()? It is an array of size (n_clusters, n_samples) and would appear to be probability values (in [0, 1]) that a given sample belongs to a given cluster. They are not log-likelihood values (since those would all be < 0). From this array, what is the correct way to compute the likelihood value needed for computing AIC? I think it is something like below, but could be wrong since I'm not yet certain of what's being returned by log_likelihood().

likelihood = vmf_soft.log_likelihood(x) # shape (n_clusters, n_samples)
log_likelihood = np.sum(np.log(np.max(likelihood, axis=0))) # Choose the cluster of highest probability, convert that probability to log-likelihood, and sum across all samples.

This is based on equation 3.2 of the 2005 paper. The cluster/class weights may need to be involved too. I'm not sure if they're already incorporated into the values returned by log_likelihood().

@jasonlaska, maybe you can help?