# Unsupervised Offline Changepoint Detection Ensembles
## 3 Results  
We provide in Tables 2 and 3 the results of the numerical experiments, in which CDP and CPDE procedures were run on the TEP and SKAB benchmarks. Negative or zeroed results mean that none of changepoints were found. Bold numbers refer to the best results among the procedure (CPD or CPDE) and search method. Dashes mean unapplicability of the cost function to the search method. It is relevant to the linear cost function and Win search method. The window-based algorithm Win when used in CPD and CPDE procedures needs an additional window width selection stage. The window width was selected from the classical grid search procedure for various values. The results are presented under the assumption that better-performed windows (\(w=20\) points) are found. The results for various windows are presented at [[https://github.com/[PERSON]/CPDE](https://github.com/[PERSON]/CPDE)]([https://github.com/[PERSON]/CPDE](https://github.com/[PERSON]/CPDE)) (accessed on 8 May 2021). One more assumption on the experiments is that various features in the datasets (signals) are generated from the various models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Metric** & \(\mathbf{A_{TP}}\) & \(\mathbf{A_{FP}}\) & \(\mathbf{A_{TN}}\) & \(\mathbf{A_{FN}}\) \\ \hline Standard & \(1.0\) & \(-0.11\) & \(1.0\) & \(-1.0\) \\ \hline LowFP & \(1.0\) & \(-0.22\) & \(1.0\) & \(-1.0\) \\ \hline LowFN & \(1.0\) & \(-0.11\) & \(1.0\) & \(-2.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Application profile for NAB scoring algorithm. \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 & & & Win\((w=20)\) & & & BinSeg & \\ \hline \multirow{3}{*}{
\begin{tabular}{c} an (1) \\ mahalanobis \\ l1 \\ linear \\ \end{tabular} } & 30.15 & 28.89 & 32.8 & 13.23 & 12.19 & 13.59 & 30.15 & 28.89 & 32.8 \\  & **36.88** & **35.82** & **37.29** & **27.79** & **27** & **28.05** & **36.88** & **35.82** & **37.29** \\  & **32.53** & 31.98 & 32.8 & 20.63 & 19.85 & 21.69 & 32.53 & 31.98 & 32.8 \\  & **30.3** & 29.52 & 31.31 & 22.09 & 21.68 & 22.66 & 30.3 & 29.52 & 31.31 \\  & **34.5** & **4.24** & **4.59** & - & - & - & 4.5 & 4.24 & 4.59 \\ \hline Aggregation & Scaling & \multicolumn{4}{c}{OptEnsemble} & \multicolumn{4}{c}{WinEnsemble (\(w=20\))} & \multicolumn{4}{c}{BinSegEnsemble} \\ \hline Min & MinMax & **41.81** & **41** & **42.16** & 23.55 & 23.28 & 23.63 & **41.81** & **41** & **42.16** \\  & Znorm & 25.66 & 24.9 & 26.63 & 23.28 & 22.76 & 23.46 & 25.66 & 24.9 & 26.63 \\  & MinAbs & 22.85 & 21.8 & 24.76 & 23.82 & 23.35 & 25.4 & 22.85 & 21.82 & 24.76 \\  & Rank & **41.81** & **41** & **42.16** & 22.93 & 22.37 & 23.23 & **41.81** & **41** & **42.16** \\ Sum & MinMax & 34.8 & 34 & 35.9 & 23.54 & 23.28 & 23.63 & 34.8 & 34 & 35.9 \\  & Znorm & 34.83 & 34.03 & 35.92 & 23.55 & 23.28 & 23.63 & 34.83 & 34.03 & 35.92 \\  & MinAbs & 34.73 & 33.68 & 35.85 & 23.68 & 22.96 & 25.31 & 34.8 & 34 & 35.9 \\  & Rank & 30.47 & 29.95 & 31.42 & 22.62 & 22.27 & 23.02 & 30.47 & 29.95 & 31.42 \\ WeightedSum & MinMax & 34.8 & 34 & 35.9 & 23.55 & 23.28 & 23.63 & 34.8 & 34 & 35.9 \\  & Znorm & 34.83 & 34.03 & 35.92 & 23.55 & 23.28 & 23.63 & 34.83 & 34.03 & 35.92 \\  & MinAbs & 34.73 & 33.68 & 35.85 & **25.14** & **24.33** & **26.29** & 34.8 & 34 & 35.9 \\  & Rank & 25.59 & 25.06 & 26.59 & 23.28 & 22.76 & 23.46 & 25.59 & 25.06 & 26.59 \\ ThresholdSum & MinMax & 33.51 & 32.58 & 35.04 & 11.46 & 10.95 & 12.4 & 33.64 & 32.73 & 35.13 \\  & Znorm & 34.83 & 34.03 & 35.92 & 11.46 & 10.95 & 12.4 & 34.83 & 34.03 & 35.92 \\  & MinAbs & \(-5.5\) & \(-11\) & \(-3.67\) & 13.75 & 13.22 & 13.93 & 33.64 & 32.73 & 35.13 \\  & Rank & \(-5.5\) & \(-11\) & \(-3.67\) & 6.38 & 5.59 & 7.43 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NAB scoring algorithm (higher is better) results of the CPD algorithms on the TEP benchmark. The best overall NAB (standard) score for TEP benchmark is equal to 41.81.