# Unsupervised Deep Anomaly Detection for Industrial Multivariate Time Series Data
## 3 Materials and Methods
### Inference
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**MBA**} & \multicolumn{4}{c}{**SMAP**} & \multicolumn{4}{c}{**SMD**} \\ \cline{2-13}  & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) \\ \hline DAGMM & 0.9475 & 0.9999 & 0.9858 & 0.9730 & 0.8069 & 0.9999 & 0.9884 & 0.8931 & 0.9402 & 0.9973 & 0.9954 & 0.9679 \\ OmniAnomaly & 0.8595 & 0.9999 & 0.9581 & 0.9244 & 0.7991 & 0.9999 & 0.9878 & 0.8883 & 0.9884 & 0.9985 & 0.9986 & 0.9934 \\ MERLIN & 0.9846 & 0.0492 & 0.5244 & 0.0937 & 0.1577 & 0.9999 & 0.7426 & 0.2725 & 0.2849 & 0.5628 & 0.7084 & 0.3783 \\ MSCRED & 0.9249 & 0.9999 & 0.9792 & 0.9610 & 0.8175 & 0.9216 & 0.9821 & 0.8664 & 0.7276 & 0.9974 & 0.9921 & 0.8414 \\ MAD-GAN & 0.9396 & 0.9999 & 0.9835 & 0.9688 & 0.8157 & 0.9999 & 0.9891 & 0.8984 & 0.9999 & 0.4023 & 0.7011 & 0.5737 \\ USAD & 0.8953 & 0.9999 & 0.9700 & 0.9447 & 0.8139 & 0.9999 & 0.9889 & 0.8974 & 0.9069 & 0.9973 & 0.9933 & 0.9499 \\ MTAD-GAT & 0.9897 & 0.9897 & 0.9973 & 0.9948 & 0.7517 & 0.9999 & 0.9840 & 0.8582 & 0.8210 & 0.9215 & 0.9921 & 0.8683 \\ CAE-M & 0.8789 & 0.9999 & 0.9647 & 0.9355 & 0.8395 & 0.9999 & 0.9907 & 0.9127 & 0.6954 & 0.9973 & 0.9933 & 0.9499 \\ GDN & 0.8441 & 0.9999 & 0.9527 & 0.9154 & 0.9476 & 0.4117 & 0.7047 & 0.5740 & 0.7169 & 0.9973 & 0.9783 & 0.8342 \\ TranAD & 0.9569 & 0.9999 & 0.9884 & 0.9779 & 0.8043 & 0.9999 & 0.9882 & 0.8915 & 0.9072 & 0.9973 & 0.9934 & 0.9501 \\ AT-DCAEP & 0.9923 & 0.9999 & **0.9980** & **0.9961** & 0.8904 & 0.9999 & **0.9940** & **0.9420** & 0.994 & 0.9981 & **0.9987** & **0.9960** \\ \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**SWaT**} & \multicolumn{4}{c}{**WADI**} & \multicolumn{4}{c}{**MSDS**} \\ \cline{2-13}  & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) & \(P\) & \(R\) & \(AUC\) & \(F1\) \\ \hline DAGMM & 0.9932 & 0.6878 & 0.8435 & 0.8128 & 0.4940 & 0.8295 & 0.9047 & 0.6192 & 0.9999 & 0.8125 & 0.9062 & 0.8965 \\ OmniAnomaly & 0.9760 & 0.6956 & **0.8465** & 0.8123 & 0.7837 & 0.6541 & 0.8249 & 0.7131 & 1.0000 & 0.7964 & 0.8982 & 0.8867 \\ MERLIN & 0.6559 & 0.2546 & 0.6174 & 0.3668 & 0.0635 & 0.7669 & 0.7499 & 0.1174 & 0.7254 & 0.3110 & 0.5022 & 0.4353 \\ MSCRED & 0.9999 & 0.6770 & 0.8385 & 0.8074 & 0.2513 & 0.7319 & 0.8412 & 0.3741 & 1.000 & 0.7983 & 0.8943 & 0.8878 \\ MAD-GAN & 0.9593 & 0.6956 & 0.8456 & 0.8064 & 0.2233 & 0.9124 & 0.8026 & 0.3588 & 0.8157 & 0.9216 & **0.9891** & 0.8654 \\ USAD & 0.9977 & 0.6878 & 0.8438 & **0.8143** & 0.1989 & 0.8295 & 0.8753 & 0.3208 & 0.7480 & 0.9627 & 0.9890 & 0.8419 \\ MTAD-GAT & 0.9760 & 0.6956 & 0.8465 & 0.8123 & 0.2818 & 0.8012 & 0.8821 & 0.4169 & 0.9997 & 0.8888 & 0.9441 & 0.9410 \\ CAE-M & 0.9593 & 0.6956 & 0.8456 & 0.8064 & 0.2782 & 0.7918 & 0.8728 & 0.4117 & 0.9999 & 0.8815 & 0.9407 & 0.9370 \\ GDN & 0.9696 & 0.6956 & 0.8462 & 0.8101 & 0.2912 & 0.7931 & 0.8777 & 0.4260 & 0.9726 & 0.8606 & 0.8988 & 0.9132 \\ TranAD & 0.9977 & 0.6878 & 0.8438 & **0.8143** & 0.3992 & 0.8295 & 0.9000 & 0.5390 & 0.9999 & 0.8125 & 0.9062 & 0.8965 \\ AT-DCAEP & 0.9977 & 0.6770 & 0.8383 & 0.8066 & 0.7880 & 0.8295 & **0.9121** & **0.8082** & 0.9924 & 0.9406 & 0.9609 & **0.9658** \\ \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of AT-DCAEP with baseline methods. \(P\): Precision, \(R\): Recall, \(AUC\): Area Under the ROC Curve, \(F1\): \(F1\) score on the entire training dataset. The best \(F1\) and \(AUC\) scores are highlighted in bold. We also conducted a study on the impact of the number of convolutional kernels on the effectiveness of anomaly detection. We configured different numbers of convolutional kernels to compare their performance in the model.