The EM algorithm is an effecive way to perform maximum
likelihood (ML) estimation when the data PDF can be easily
maximized if a certain set of unknown parameters are known.
These ``unknown" parameters, or missing data, are the mode assignments.
The mode assignments can be understood if we assume that each
data sample from the Gaussian mixture had been produced by exactly one
of the modes. The mode assignment for sample is denoted and
denotes a particular set of assignments
Gaussian Mixtures and the E-M Algorithm