Biometric Authentication: A Machine Learning Approach

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 = {x_t ∊ ℜ^D; t = 1, …, T} is the observation sequence, where T is the number of observations and D is the dimensionality of x_t.

• C = {C⁽¹⁾, …, C^(J)} is the set of cluster mixture labels, where J is the number of mixture components.

• Z = {z_t ∊ 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 ...