How does BIC choose k in GMM?

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Answer

$BIC = -2 log L + p log n where p = number of free parameters, n = dataset size.$
$Lower is better.$
$Balances fit (log L) against complexity (p log n).$
$For GMM, p grows with k and covariance type.$
$K_{\mathrm{max}}$
$More reliable than AIC for clustering.$

Check yourself — multiple choice

Higher BIC is better
BIC = -2 log L + p log n; fit at k=1.. $K_{\mathrm{max}}$ , pick minimum; balances fit vs complexity → standard for GMM k selection
Same as elbow
Random

BIC in GMM: minimize -2 log L + p log n over k.

#clustering#density#evaluation

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