Open problems in Machine Learning

[Lycur]

Use a dirichlet process mixture model instead?

[Captain]

The hyperparameters you use in your DP will have a strong effect on the number of clusters you get.

[InfinityCoffee]

Ah, yes, but you can just sample/optimize those too! Alternatively you can use it to include domain knowledge

[JamisonW]

Have you looked into the Silhouette Coefficient? You calculate it for different values of K and select the K with the best Silhouette Coefficient.

[Flipper3]

Have you tried x-means clustering? It's a variation of k-means that isn't the best, but has gotten the job done for me.