Biometric Authentication: A Machine Learning Approach

3.3. An Entropy Interpretation

The previous section has shown that the EM algorithm is a powerful tool in estimating the parameters of finite-mixture models. This is achieved by iteratively maximizing the expectation of the model's completed-data likelihood function. The model's parameters, however, can also be obtained by maximizing an incomplete-data likelihood function, leading to an entropy interpretation of the EM algorithm.

3.3.1. Incomplete-Data Likelihood

The optimal estimates are obtained by maximizing

Equation 3.3.1

Define

such that ...