Example:

Suppose f_i for are M₁ training vectors quantised to first reconstruction level .The new estimate of is obtained by minimizing . If used is the squared error , then the new estimate of just the average of M, training vectors  for ;

To show this,

consider

i.e.

Minimising we have,

A new estimate of all other reconstruction level for , is similarly obtained. This completes one iteration of the procedure, which can be stopped when average distortion D does not change significantly between two consecutive iteration.

Due to the clustering involved, this also is as clustering algorithm in pattern recognition iteration.

The flow graph representation of K-means algorithm.