Biometric Authentication: A Machine Learning Approach

Appendix A. Convergence Properties of EM

The EM algorithm is a general technique for maximum-likelihood estimation (MLE). This appendix provides proof showing that the likelihood function is guaranteed to increase during EM learning. For more convergence properties of the EM algorithm, see [74, 350, 389].

Because sample density p(x(t)|ω) depends on the parameters w, the density function can be rewritten as

For simplicity, the indicator w is omitted:

Following the preceding notation, the log-likelihood to be maximized is rewritten as

Equation ...