Derivation of the Hierarchical EM algorithm for Dynamic Textures

This is the supplemental material for the CVPR 2010 paper, “Clustering Dynamic Textures with the Hierarchical EM Algorithm” [1]. It contains the derivation of the HEM-DTM algorithm and the associated E-step computations, including sensitivity analysis for the Kalman smoothing filter. 1 Derivation of HEM for dynamic textures In this section we derive the HEM algorithm for dynamic textures. We begin with the derivation of the Q function, followed by the Eand M-steps. 1.1 Q function for HEM-DTM In the E-step, the Q function is obtained by taking the conditional expectation, with respect to the hidden variables {X,Z}, of the complete-data likelihood in (7) Q(Θ(r), Θ̂) = K(b) ∑

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