# Unsupervised Offline Changepoint Detection Ensembles
## 3 Results
### CPD and CPDE Procedures  
For TEP, Opt shows exact results as BinSeg, while OptEnsemble shows quite similar results to BinSegEnsemble. As for SKAB, the difference between Opt and BinSeg is minor as well, while the difference between OptEnsemble and BinSegEnsemble is already significant in favor of the first. It is interesting that OptEnsemble improves Opt for both benchmarks, and BinSegEnsemble improves BinSeg just for TEP. Especially interesting is that BinSegEnsemble shows excellent results for TEP, demonstrating much better performance than BinSeg and has great results in general, but BinSegEnsemble for SKAB loses against the BinSeg algorithm as well as generally among all CPDE procedures. We can explain it by benchmark differences and fitting of the specific algorithms to the data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Standard** & **LowFP** & **LowFN** & **Standard** & **LowFP** & **LowFN** & **Standard** & **LowFP** & **LowFN** \\ \hline Model & & Opt & & & & & BinSeg & & \\ \hline ar (1) & 19.4 & 16.83 & 20.63 & 12.36 & 9.58 & 13.62 & 21.39 & 18.89 & 22.72 \\ mahalanobis & **22.37** & **19.9** & **23.37** & 15.55 & 13.44 & 16.27 & **24.1** & **21.69** & **25.04** \\ l1 & 18.64 & 15.99 & 20.12 & **18.4** & **16.22** & **19.19** & 17.87 & 15.1 & 19.09 \\ l2 & 18.96 & 16.5 & 20.33 & 14.78 & 12.4 & 16.01 & 17.46 & 14.81 & 18.82 \\ linear & 9.37 & 6.6 & 10.61 & - & - & - & 9.53 & 6.7 & 10.97 \\ \hline Aggregation & Scaling & & OptEnsemble & & & & BinSegEnsemble & & \\ \hline Min & MinMax & 19.77 & 17.04 & 20.87 & 14.41 & 11.88 & 15.51 & 0.18 & -4.69 & 1.91 \\  & Znorm & 17.71 & 15.01 & 18.99 & 15.85 & 13.19 & 16.98 & 13.03 & 10.85 & 14.07 \\  & MinAbs & 19.33 & 16.67 & 20.83 & 16.51 & 13.92 & 17.68 & 7.05 & 3.98 & 8.55 \\  & Rank & 19.77 & 17.04 & 20.87 & 16.08 & 13.22 & 17.39 & 0.6 & -3.84 & 2.19 \\ Sum & MinMax & 20.52 & 18.09 & 21.88 & 16.7 & 14.54 & 17.54 & 15.71 & 13 & 16.89 \\  & Znorm & 20.89 & 18.46 & 22.13 & 16.14 & 13.85 & 16.91 & 11.64 & 10.24 & 12.12 \\  & MinAbs & 20.25 & 17.95 & 21.45 & **19.38** & **17.03** & **20.35** & 15.84 & 13.26 & 16.97 \\  & Rank & 21.53 & 18.98 & 22.82 & 14.25 & 11.5 & 15.39 & 10.15 & 8.29 & 11.12 \\ WeightedSum & MinMax & 21.24 & 18.77 & 22.62 & 15.31 & 12.94 & 16.1 & 16.41 & 13.95 & 17.6 \\  & Znorm & 20.89 & 18.46 & 22.13 & 14.08 & 11.6 & 15.03 & 15.3 & 12.74 & 16.61 \\  & MinAbs & 20.16 & 17.78 & 21.39 & 18.58 & 16.19 & 19.57 & 16.41 & 13.95 & 17.6 \\  & Rank & **23.07** & **20.52** & **24.35** & 12.9 & 10.22 & 13.99 & **18.1** & **15.36** & **19.51** \\ ThresholdSum & MinMax & 21.2 & 18.69 & 22.6 & 9.5 & 7.31 & 10.69 & 15.71 & 13 & 16.89 \\  & Znorm & 21.7 & 19.32 & 22.93 & 10.06 & 7.93 & 11.32 & 11.64 & 10.24 & 12.12 \\  & MinAbs & \(-5.5\) & \(-11\) & \(-3.67\) & 9.96 & 6.91 & 11 & 15.8 & 13.17 & 16.94 \\  & Rank & \(-5.5\) & \(-11\) & \(-3.67\) & 10.87 & 7.98 & 12.12 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: NAB scoring algorithm (higher is better) results of the CPD algorithms on SKAB.  
Win algorithm is the only algorithm among non-ensemble ones that outperforms ensemble procedures for the TEP benchmark. Even so, for SKAB, WinEnsemble outperforms the Win algorithm quite confidently, which can also be explained by the overfitting to the data. Eventually, Win and WinEnsemble display the weakest performance among all CPD and CPDE procedures.  
Finally, in four out of six cases, the ensemble approach shows better results than the non-ensemble one, and one of the other two cases is comparable. Therefore, there is just one (out of six) considerable loss of the ensemble approach against the non-ensemble ones. OptEnsemble demonstrates the best overall performance regardless of the benchmark, aggregation, or scaling function.