3.2. Traditional Derivation of EM
Each EM iteration is composed of two steps—Estimation (E) and Maximization (M). The M-step maximizes a likelihood function that is further refined in each iteration by the E-step. This section derives the traditional EM and establishes its convergence property.
3.2.1. General Analysis
The following notations are adopted.
X = {xt ∊ ℜD; t = 1, …, T} is the observation sequence, where T is the number of observations and D is the dimensionality of xt.
C = {C(1), …, C(J)} is the set of cluster mixture labels, where J is the number of mixture components.
Z = {zt ∊ C; t = 1, …, T} is the set of missing data (specifying the hidden-state information).
θ = {θ(j); j = 1, …, J} is the set of unknown parameters that define the ...
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