I suspect the AIC/BIC values for GMM clustering are suggesting too high a number of clusters, in the sense that they are probably overfitting (with only a few values in some clusters). What are some limitations of using AIC/BIC and why should one look to other measures such as Silhouette method to choose the number of clusters?
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I am not familiar with GMM, but have worked with AIC and BIC criteria. AIC and BIC provide in essence corrections for the number of parameters in a model so to prevent overfitting.
The best would be for example in an hierarchical regression model (where the larger regression model has all the parameters of the smaller model, plus one extra parameter) to perform a significance test that determines if the added parameter of the larger model adds value.
BIC and AIC are (rational) rules of the thumb (or heuristics) that can be applied in absence of a real test. Applying BIC or AIC is better than applying no rule; in practice though your mileage may vary since the penalties applied for extra parameters by both AIC and BIC are generalized rules. Another method might be better suited for your case; such is the nature of heuristics.
