Editing Mixture model (section)

===Handwriting recognition===
The following example is based on an example in [[Christopher M. Bishop]], ''Pattern Recognition and Machine Learning''.<ref>{{cite book | last = Bishop | first = Christopher | title = Pattern recognition and machine learning | publisher = Springer | location = New York | year = 2006 | isbn = 978-0-387-31073-2 }}</ref>

Imagine that we are given an ''N''×''N'' black-and-white image that is known to be a scan of a hand-written digit between 0 and 9, but we don't know which digit is written.  We can create a mixture model with <math>K=10</math> different components, where each component is a vector of size <math>N^2</math> of [[Bernoulli distribution]]s (one per pixel).  Such a model can be trained with the [[expectation-maximization algorithm]] on an unlabeled set of hand-written digits, and will effectively cluster the images according to the digit being written.  The same model could then be used to recognize the digit of another image simply by holding the parameters constant, computing the probability of the new image for each possible digit (a trivial calculation), and returning the digit that generated the highest probability.