Fig. 1

Illustration of EDHMM structure, with example of \({\textbf{K}}_3=\{K_1,K_2,K_3\}\) and \({\textbf{X}}_5=\{X_1,\ldots ,X_5\}\), hence \(M=3\), \({\bar{D}}=2\) and \(N=5\). States in the upper half represent \((K_m,d=1)\) while states in lower half represent \((K_m,d=2)\). The blue path goes through five states \((K_1,d=2),(K_1,d=1),(K_2,d=2),(K_2,d=1),(K_3,d=1)\), representing the sequence of pairs \((K_1,D_1=2), (K_2,D_2=2), (K_3,D_3=1)\); The yellow path goes through \((K_1,d=1),(K_2,d=1),(K_3,d=2),(K_3,d=2),(K_3,d=1)\), representing the sequence of pairs \((K_1,D_1=1), (K_2,D_2=1), (K_3,D_3=3)\)