# Outlier Detection for Multivariate Time Series Using Dynamic Bayesian Networks
## 4 Experimental Results
### Simulated Data
#### 4.1.3 Comparison between GMM and [PERSON]'s Score-Analysis  
With the aim of giving additional insight on which method to choose when performing score-analysis and summarize the conclusions derived from the experimental results using simulated data, the F\({}_{1}\) scores for each method are compared in the presence of different outlier ratios.  
In Figure 4, the average F\({}_{1}\) scores of every experiment using a specific method and outlier ratio is shown. [PERSON]'s method performs very poorly in datasets with 20% of anomalies while outperforming the GMM strategy in datasets with 5% of anomalies as well as control experiments.  
To determine a priori which method will excel in the score-analysis of a specific dataset, analysts should understand the underlying process generating normal data and the ability to anticipate the type of outlier expected. [PERSON]'s method expects score distributions to be negatively skewed, meaning that anomalies are generated by the same underlying process as normal data but present the lowest distribution scores. These scenarios are the most common, being real-world examples studied in Sections 4.2 and 4.3. Alternatively, if a different external process is generating abnormal data that contaminates the rest of the data, the score distribution of the whole dataset will present multiple clusters requiring the employment of the GMM method to separate both classes. An example is seen in the experiments using simulated data where GMM performs well regard  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Model B**} & \multicolumn{4}{c}{**Model C**} \\ \hline \(P_{O}\) & \(N\) & **PPV** & **TPR** & **ACC** & **F\({}_{1}\)** & \(N\) & **PPV** & **TPR** & **ACC** & **F\({}_{1}\)** \\ \hline \multirow{3}{*}{5} & 100 & 0.82 & 0.70 & 0.98 & 0.76 & 100 & 0.64 & 1.00 & 0.96 & 0.78 \\  & 1000 & 0.91 & 0.97 & 0.99 & 0.94 & 1000 & 0.86 & 0.99 & 0.99 & 0.92 \\  & 10,000 & 0.95 & 0.98 & 0.99 & 0.96 & 10,000 & 0.98 & 1.00 & 0.99 & 0.99 \\ \hline \multirow{3}{*}{10} & 100 & 0.77 & 0.68 & 0.93 & 0.72 & 100 & 0.92 & 0.78 & 0.97 & 0.84 \\  & 1000 & 0.94 & 0.96 & 0.99 & 0.95 & 1000 & 0.89 & 0.97 & 0.98 & 0.93 \\  & 10,000 & 0.91 & 0.98 & 0.99 & 0.94 & 10,000 & 0.93 & 0.96 & 0.99 & 0.95 \\ \hline \multirow{3}{*}{20} & 100 & 0.66 & 0.49 & 0.85 & 0.56 & 100 & 0.75 & 0.58 & 0.88 & 0.65 \\  & 1000 & 0.86 & 0.89 & 0.94 & 0.87 & 1000 & 0.91 & 0.92 & 0.96 & 0.92 \\ \cline{1-1}  & 10,000 & 0.86 & 0.94 & 0.96 & 0.90 & 10,000 & 0.93 & 0.94 & 0.97 & 0.94 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Subject outlier detection of METEOR on simulated data using GMM’s strategy.  
Figure 4: Comparison between GMM and [PERSON]’s score-analysis F\({}_{1}\) scores for multiple outlier ratios. Each value is an average of all 15 trials performed for each outlier ratio.  
Although the present synthetic experiments seem to endorse the use of a GMM strategy, one should note that both normal and abnormal data are generated according to two defined models, which can, by some degree, be separated. Such is a favorable scenario for GMM. When considering other scenarios, [PERSON]'s method is not so susceptible to well-defined curves being thus always a strategy to consider. With that said, it is advised for the analyst to apply as much knowledge as possible with both strategies' experimentation.