I have recently been trying to understand the X-means method for deciding on K, using BIC. However I have become stuck on one particular equation in the original paper. On the 4th page, when discussing BIC calculations, the authors write:

Focusing just on the set $D_n$ of points which belong to centroid $n$ and plugging in the maximum likelihood

What do they mean by 'centroid $n$'?

My initial intuition was one of the clusters in the model. However if this is true, why does likelihood equation for $D_n$ include K? Because we have subset to a single cluster, this would always be 1. So this cannot be the correct interpretation.

The full equation is:

$l_{hat}(D_n) = -R_n / 2 * log(2 \pi) - R_n M / 2* log(\sigma_{hat}^2) - R_n - K / 2 + R_nlogR_n - R_n log R $

Which is the last equation on the first column of page 4.

There are two other questions around BIC calculations in X-Means, but I don't think they explain this particular point:

X-Means Calculation of BIC

X-mean algorithm BIC calculation question


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.