## 4 Experimental Results and Discussion
### Experimental Results
#### 4.3.2 Additional Experimental Results and Analysis of Running Time  
To further test the scalability of the ISOD algorithm, the running time of the algorithm on the 10 datasets mentioned above was tested, and the results are represented in the form of a scatter plot, as shown in Figure 1. In this figure, the horizontal axis represents the size of the dataset, the vertical axis represents the dimensionality of the data, and the dot size represents the running time of the ISOD algorithm on the dataset. The larger the dot, the longer the running time.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & **KNN** & **LOF** & **IForst** & **CBLOF** & **LSCP** & **OCSVM** & **DIF** & **GANomaly** & **ISOD** \\ \hline Musk & 0.73 & 0.86 & 0.709 & 0.755 & 0.472 & 0.111 & 0.874 & 0.248 & **0.956** \\ \hline Satimage-2 & 0.144 & 0.19 & 0.557 & 0.28 & 0.77 & 0.274 & 0.535 & **0.929** & 0.775 \\ \hline Letter Recognition & 0.364 & 0.121 & 0.105 & 0.202 & 0.2 & 0.323 & 0.486 & 0.152 & **0.797** \\ \hline Speech & 0.755 & 0.406 & 0.278 & 0.918 & 0.981 & 0.58 & 0.736 & 0.692 & **0.833** \\ \hline Satellite & 0.625 & 0.393 & 0.475 & 0.664 & 0.837 & 0.593 & 0.22 & 0.58 & **0.9** \\ \hline Arrhythmia & 0.769 & 0.433 & 0.168 & 0.798 & 0.297 & 0.171 & **0.91** & 0.324 & 0.538 \\ \hline Ionosphere & 0.238 & 0.846 & 0.272 & 0.343 & 0.605 & 0.867 & 0.127 & 0.165 & **0.912** \\ \hline Mnist & 0.476 & 0.454 & 0.115 & 0.369 & 0.418 & **0.904** & 0.787 & 0.603 & 0.808 \\ \hline Optdigits & 0.794 & 0.478 & 0.798 & 0.518 & 0.264 & 0.896 & **0.924** & 0.67 & 0.747 \\ \hline Heart & 0.705 & 0.331 & 0.488 & 0.115 & 0.311 & 0.56 & 0.355 & 0.429 & **0.863** \\ \hline Average ROC & 0.56 & 0.451 & 0.397 & 0.496 & 0.516 & 0.528 & 0.545 & 0.479 & **0.813** \\ \hline \hline \end{tabular}
\end{table}
Table 2: ROC scores in terms of outlier detector performance (the highest ROC scores are marked in bold).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Dataset** & **KNN** & **LOF** & **IForst** & **CBLOF** & **LSCP** & **OCSVM** & **DIF** & **GANomaly** & **ISOD** \\ \hline Musk & 0.589 & 0.756 & 0.115 & 0.397 & 0.432 & 0.143 & 0.272 & 0.66 & **0.814** \\ \hline Satimage-2 & 0.188 & 0.321 & 0.786 & 0.146 & 0.154 & 0.315 & 0.494 & 0.807 & **0.856** \\ \hline Letter Recognition & 0.257 & 0.474 & 0.948 & 0.52 & **0.964** & 0.885 & 0.802 & 0.345 & 0.754 \\ \hline Speech & 0.536 & 0.214 & 0.195 & 0.138 & 0.32 & 0.164 & 0.349 & 0.822 & **0.996** \\ \hline Satellite & 0.281 & 0.794 & 0.321 & 0.204 & 0.633 & 0.737 & **0.962** & 0.888 & 0.887 \\ \hline Arrhythmia & 0.207 & 0.103 & 0.612 & 0.534 & 0.407 & 0.338 & 0.422 & 0.551 & **0.663** \\ \hline Ionosphere & 0.929 & **0.985** & 0.979 & 0.138 & 0.827 & 0.88 & 0.715 & 0.741 & 0.566 \\ \hline Mnist & **0.744** & 0.271 & 0.679 & 0.592 & 0.604 & 0.274 & 0.433 & 0.605 & 0.392 \\ \hline Optdigits & 0.264 & 0.656 & 0.359 & 0.221 & 0.394 & 0.261 & 0.553 & 0.112 & **0.776** \\ \hline Heart & 0.439 & 0.511 & 0.32 & 0.734 & 0.208 & 0.387 & 0.796 & 0.794 & **0.8** \\ \hline Average ROC & 0.443 & 0.509 & 0.531 & 0.362 & 0.494 & 0.438 & 0.58 & 0.632 & **0.75** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average precision (AP) scores in terms of outlier detector performance (the highest AP scores are marked in bold).  
Although Figure 1 does not provide a specific running time, by comparing the size of these scatter plots, we can see that a dataset with a large amount of data or data with a high dimensionality has a longer running time for the ISOD algorithm, which conforms the complexity analysis results mentioned earlier.