Apparently, adding the loading factor to the covariance matrix does impact the log-likelihood value. I made some experiments on the issue, and let me share the results with you as seen in the learning curve (log-likelihood curve) of ITSBN with EM algorithm below. The factor is applied to the matrix only when the determinant of the covariance matrix is smaller than $10^{-6}$. There are 5 different factors used in this experiment listed as follows; $10^{-8}, 10^{-6}, 10^{-4}, 10^{-3}, 10^{-2}$. The results show that the learning curves are still monotonically increasing* and level off near the end. Furthermore, we found that the level-off value are highly associated with the value of the factor. The bigger the factor, the smaller the level-off value. This suggested that we should pick smallest value of factor as possible in order to stay as close as the ideal learning curve as possible. Note that the loading factor is not added to the covariance matrix until the second iteration.