# Tri-Partition Alphabet-Based State Prediction for Multivariate Time-Series
## 5 Experiments
### Stability  
Tables 7 and 8 list the top 10 metric combinations for precision and recall with four kinds of states on the four datasets' test sets. We can observe that some metric combinations are repeated. Hence, these combinations are considered more stable, with higher frequency/probability occurring in different datasets. For stronger discrimination, we additionally introduce a weighting strategy ranking for each metric combination. Given a metric combination \(x\in[0,9]\):  
\[\rho(x)=\frac{\xi(x)}{2^{\pi(x)}} \tag{24}\]  
is the stability metric of \(x\). Among them, \(\xi(x)\) is the occurrence on four datasets. Moreover:  
\[\pi(x)=\frac{\Sigma_{i\in\{\text{I, II, III, IV}\}}\eta(x,i)}{\xi(x)} \tag{25}\]  
is the average ranking of \(x\). If \(x\) does not occur in dataset \(i\), \(\eta(x,i)=0\). Otherwise, \(\eta(x,i)\) is the ranking of \(x\). Figure 5: The recalls of four state prediction strategies. (**a**) Dataset I. (**b**) Dataset II. (**c**) Dataset III. (**d**) Dataset IV. Figure 6 shows the most stable metric combinations for precision. In terms of the state, combination \((1,8)\) is the first choice. In terms of the tri-state, combination \((1,8)\) is the first choice. In terms of the IFS-based tri-state, combination \((3,8)\) is the first choice. In terms of the RFS-based tri-state, combination \((3,8)\) is the first choice. Figure 7 shows the most stable metric combinations for recall. In terms of the state, combination \((1,8)\) is the first choice. In terms of the tri-state, combination \((1,8)\) is the first choice. In terms of the IFS-based tri-state, combination \((0,8)\) is the first choice. In terms of the RFS-based tri-state, combination \((0,8)\) is the first choice. In terms of the RFS-based tri-state, combination \((9,8)\) is the first choice. With the above observations, the eighth metric, i.e., the Jaccard similarity, is the most frequently used, followed by the second one, i.e., the Manhattan distance. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Dataset** & **Type of State** & **Metric Combinations (\(r,c\))** \\ \hline I & State & (5, 1), (7, 1), (4, 1), (7, 8), (3, 7), (9, 1), (1, 8), (5, 8), (1, 7), (0, 8) \\  & Tri-state & (9, 1), (9, 8), (3, 8), (5, 1), (7, 8), (3, 0), (7, 1), (4, 1), (4, 7), (3, 1) \\  & IFS-tri-state & (3, 8), (9, 1), (9, 8), (5, 1), (3, 0), (7, 8), (8, 8), (7, 1), (4, 1), (4, 7) \\ II & State & (1, 8), (1, 7), (5, 0), (7, 0), (4, 0), (0, 7), (7, 0), (9, 1), (4, 1), (0) \\  & Tri-state & (7, 7), (9, 0), (8, 8), (1, 7), (8, 1), (1, 1), (1, 3), (1, 9), (1, 8), (9, 8) \\  & IFS-tri-state & (7, 7), (3, 0), (1, 3), (7, 1), (4, 1), (0), (1, 8), (1, 9), (1, 3), (1, 1) \\  & RFS-tri-state & (0, 0), (3, 1), (0, 7), (5, 0), (4, 1), (5, 7), (1, 0), (1, 7), (9, 1), (1, 3) \\ III & State & (7, 8), (0, 8), (7, 4), (4, 1), (1, 8), (4, 8), (7, 7), (1, 7), (7, 9), (8, 8) \\  & Tri-state & (9, 8), (3, 3), (1, 7), (8, 8), (1, 4), (7, 8), (0, 4), (8, 4), (8, 0) \\  & IFS-tri-state & (3, 3), (7, 8), (4, 8), (9, 8), (1, 8), (0, 8), (8, 8), (9, 7), (1, 4), (0, 4) \\  & RFS-tri-state & (1, 8), (9, 8), (8, 1), (0, 7), (0, 1), (1, 4), (0, 8), (1, 0), (0, 4), (1, 1) \\ IV & State & (0, 1), (0, 7), (0, 0), (1, 0), (5, 7), (3, 7), (5, 0), (1, 1), (7, 1), (7, 0) \\  & Tri-state & (7, 7), (5, 7), (4, 0), (5, 0), (0, 0), (5, 1), (0, 7), (4, 7), (4, 1), (7, 0) \\  & RFS-tri-state & (5, 7), (4, 4), (0, 7), (7, 1), (7, 8), (7, 0), (5, 1), (5, 0), (5, 4), (4, 0) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The top 10 metric combinations for precision.