# X-Means Calculation of BIC

I am trying to calculate the BIC for the X-Means algorithm as described in the paper by Pelleg and Moore (https://www.cs.cmu.edu/~dpelleg/download/xmeans.pdf).

The paper describes the calculation of the pj variable, which I do not understand completely:

The number of free parameters pj is simply the sum of K-1 class probabilities, M*K centroid coordinates, and one variance estimate.

On another post (X-mean algorithm BIC calculation question), a user described the calculated of pj as simply K-1 + M*K + 1. I am wondering if anyone has any knowledge as to whether this is correct or not?

The two sources you cite give the same answer: $p_j$ is the number of free parameters in a model with $K$ clusters:
• $K-1$ cluster probabilities (the $K^{th}$ being forced because they sum to $1$)
• $MK$ centroid coordinates ($K$ centroid, each with $M$ features)
• $1$ variance estimate, assuming common covariance (per answer to the linked question)