Algorithm 1 Health State Partitioning

1: Input: HI_sequence, M, ${\epsilon }_{\max }$

2: Output: S (Final Segmentation)

3: Initialize:

4:   $S=\left\{s_1,s_2,···,s_N\right\}$$, \mathrm{where} \mathrm{each} s_i$, is a data point from HI_sequence.

5:    Q = Priority Queue of pairs $\left(C\left(s_j,s_{j+1}\right),s_j,s_{j+1}\right)$ for all adjacent pairs.

6:    $C\left(s_j,s_{j+1}\right)$= merge cost function $\left(s_j,s_{j+1}\right)$

7: Iterative Merging:

8: while  $\left|S\right|>M$ and $\max \left({\epsilon }_i\right)>{\epsilon }_{\max }$ do

9.         $\left(C_{\min },s_m,s_{m+1}\right)=Q$

10:         ${s^{\prime }}_m=merge\left(s_m,s_{m+1}\right)$ {Merge segments}

11:         Update Queue:

12:         Remove old pairs costs: $C\left(s_{m-1},s_m\right),C\left(s_m,s_{m+1}\right),C\left(s_{m+1},s_{m+2}\right)$

13:         Insert new costs: $C\left({s^{\prime }}_{m-1},{s^{\prime }}_m\right),C\left({s^{\prime }}_m,{s^{\prime }}_{m+1}\right)$

14: end while

15: Termination:

16: if  $\left|S\right|\le M$ or $\max \left({\epsilon }_i\right)\le {\epsilon }_{\max }$ then

17:    Stop

18: end if

19: Output:$S=\left\{s_1,s_2,···,s_M\right\}$.