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I have applied GMM(Gaussian Mixture Model) to my data set and I have plotted the resulting BIC(Bayesian Information Criterion) and AIC(Akaike Information Criterion) for different number of components. I would like to know how can I find the best heuristc number of components using BIC and AIC plots. Following paper suggests to look at the first local maxima in the plot but I do not know why? https://www.ics.uci.edu/~smyth/courses/cs274/readings/fraley_raftery.pdf

Here is the plot that I get : is lower BIC or AIC better? so I need 7 components.

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  • $\begingroup$ I think the idea is to look for the "elbow" in the BIC curve, or where the gradient stops decreasing. In your case its 3. Increasing the number of components increases the log likelihood, but this should be penalized. See towardsdatascience.com/… $\endgroup$ – Zeus Aug 21 '19 at 3:28

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