# Information Extraction from Industrial Sensor Data Using Time Series Meta-Features
## 3 Approach  
The iterative approach visualized in Figure 3 is not specifically tailored to the aluminum electrolysis process and can be applied to different fields of the smart manufacturing sector. With our approach, we wanted to assess the suitability of PCA and time series meta-features in the aluminum industry. This gives us a baseline that we can use for a comparison with future methods. At first, several time series meta-features are calculated for each time series in a data set and are saved as a meta-feature data set. Although it is presented in the context of meta-learning, the guideline in [25] is also helpful to find appropriate meta-features. The guideline points out that a manageable amount of meta-features \begin{table}
\begin{tabular}{c c} \hline \hline
**Domain** & **Literature** \\ \hline Regression & [16] \\ \hline Classification & [17; 20] \\ \hline Clustering & [21] \\ \hline Anomaly detection & [15; 22] \\ \hline Visualization & [23] \\ \hline Meta-learning & [9; 25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Literature addressing the calculation of time series meta-features in six different domains. already used in the literature should be considered in the analysis. Additionally the type of each time series in the data set should be incorporated in the selection of meta-features. In the next step, a PCA is conducted using the z-transformed meta-features. PCA has already been successfully applied in [15; 23] to identify data patterns by projecting time series meta-features into a lower feature space. Therefore, we decided to apply PCA to the aluminum electrolysis process. Afterward, the first two principal components are used to generate a two-dimensional feature space that visualizes the characteristics of the time series data set. We chose a two-dimensional representation because it is easier to analyze for salient time series than three- or four-dimensional feature spaces. Higher dimensions lead to increased complexity, for which suitable representations should be reviewed. Each point in the two-dimensional feature space represents a time series. The feature space helps to find time series with abnormal characteristics, e.g., implausible ranges of values, compromising the feature space. Hence, the corresponding instances (rows) should be removed from the meta-feature data set. It is not necessary to identify all abnormal time series and to remove the corresponding meta-feature instances from the data set in the first iteration because further iterations are conducted (see Figure 3). The iteration process can be stopped if one is convinced that all compromising meta-feature instances have been removed from the data set. This constitutes a soft breaking parameter: the more compromising instances are removed, the more accurate the resulting insights are to be expected. Conversely, this means: Stopping too early only influences the details of the insights but not the overall results. The identification of abnormal time series in the two-dimensional plot depends on the human operator using our approach. We are aware that this step is not optimal and should be addressed in further research. Generating multiple feature spaces has several advantages: Implausible time series indicate detached or faulty sensors, which can be quickly identified by analyzing the feature spaces. This can help process engineers save time because they will not have to check  
Figure 3: The flow chart shows each step of the approach. A set of time series meta-features is calculated, which should describe the characteristics of the time series data set. Using the calculated meta-features, a principal component analysis (PCA) is conducted to create a two-dimensional feature space, which is used to identify implausible time series. The corresponding instances (rows) are removed from the meta-feature data set and further iterations are performed until all implausible time series have been identified. hundreds of time series to find salient sensors manually.