Multi tool use

Should BIC (Bayesian Information Criterion) be lower or higher

I am very confused about the BIC plots vs number of components in GMM. Python documentation is saying the lower the better but I read in some websites that the correct number of clusters is the first location of local maxima !!!

Can anyone elaborate on that, is Python using different equations perhaps with minus sign multiplied to the BIC score equation ?

1 Answer
1

It seems BIC definition changes on different sources. Here is source code of bic method :

def bic(self, X):
. . .
return (-2 * self.score(X) * X.shape[0] +
self._n_parameters() * np.log(X.shape[0]))


As complexity of the model increases, bic value increases and as likelihood increases, bic decreases. So, lower is better.
This definition is same as the formula on related the wikipedia page.

Also, I found this note on the wikipedia page which may explain why this definition is minus of what you expected:

NOTE: The AIC, AICc and BIC defined by Claeskens and Hjort (2008) is the negative of that defined in this article and in most other standard references.

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