Editing Mixture model (section)

==== The maximization step ====
With expectation values in hand for group membership, [[plug-in estimates]] are recomputed for the distribution parameters.

The mixing coefficients ''a<sub>i</sub>'' are the [[arithmetic mean|mean]]s of the membership values over the ''N'' data points.

:<math> a_i = \frac{1}{N}\sum_{j=1}^N y_{i,j}</math>

The component model parameters ''θ<sub>i</sub>'' are also calculated by expectation maximization using data points ''x<sub>j</sub>'' that have been weighted using the membership values.  For example, if ''θ'' is a mean ''μ''

:<math> \mu_{i} = \frac{\sum_{j} y_{i,j}x_{j}}{\sum_{j} y_{i,j}}.</math>

With new estimates for ''a<sub>i</sub>'' and the ''θ<sub>i</sub>'''s, the expectation step is repeated to recompute new membership values.  The entire procedure is repeated until model parameters converge.