I am curious to explore the connection between this paper and regularized versions of the EM algorithm. The EM algorithm is employed to obtain the maximum likelihood estimate of mixture model parameters which best explains the unknown probability density of given data. Loosely speaking a gaussian mixture model tends to approximate an unknown probability density function which is available to us only in the form of examples.

Sometimes. it is possible that we have an apriori knowledge about the pdf of the source. In such cases, usually a prior is assumed on the mixture model parameters and the Maximum aposteriori estimate is obtained recursively using the EM. This connects to the correspondence between bayesian networks and reguralization networks pointed out in the paper.

In the light of this paper we may obtain alternate versions of the EM by setting it in a regularization framework. However i feel there are no specific advantage to doing so since both approaches seem equivalent.

Nonetheless the geometric interpretation in terms of kernel basis functions can shed more light on how assuming a prior influences the estimation.