# Bootstrap-CURE: A Novel Clustering Approach for Sensor Data--An Application to 3D Printing Industry
## 6 Applications to 3D Printer Data
### Post-Processing in Bootstrap-CURE Method  
Post-processing of bootstrap-CURE dataset is accompanied with the class panel graph. Figure 9 shows part of the class panel graph from final data (with vertical scales of all cells normalized to a range of [0-1]). The conditional distribution of sensor_1 to sensor_5 exhibits a similar behavior as observed in the work [9]. To compare hierarchical clustering with the _bootstrap_-_CURE_ strategy, the authors focus on the 10,000 elements common between both experiments. Table 3 shows that class 0 of both clustering approaches is distributed among the other classes, thereby showing some differences in the results for both strategies. The objects included in each cluster are not exactly the same. However, 81.36% of the printing jobs data match in the same class for both hierarchical clustering and _bootstrap_-_CURE_, strengthening our proposal. Figure 8: CPU time comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Bootstrap–CURE**} \\  & & **Cluster 0** & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline \multirow{4}{*}{**Hierarchical Clustering**} & Cluster\_0 & 1476 & 549 & 770 & 133 \\  & Cluster 1 & 157 & 2324 & 0 & 0 \\ \cline{1-1}  & Cluster 2 & 201 & 0 & 2639 & 0 \\ \cline{1-1}  & Cluster 3 & 54 & 0 & 0 & 1697 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cluster evaluation between hierarchical and bootstrap–CURE. Table 4 compares the _Calinski-Harabasz_ (_CH_) indices between the original sample using the classical hierarchical algorithm, original CURE and the _bootstrap-CURE_ proposal. The _CH_ index obtained on the _bootstrap-CURE_ clustering is much lower than the same obtained in [9], using hierarchical clustering. It is to be noted that the _bootstrap-CURE_ method is computationally much less expensive, as the assignment of labels does not need the whole  
Figure 9: Class panel graph for selected sensors. set of rows to be used in clustering. This is particularly useful to approximate large data by a substantially lesser number of records to process in clustering. Hence, the profiles discovered by both of the approaches maintain stable clusters; however, the ones obtained by the _bootstrap-CURE_ method are more relevant for the big data framework, as they are based on the larger dataset size and most of the clusters show smaller standard deviations as well. Illustrative variables are also used to help understand the structure of the clusters (see Figure 10 for job status by clusters and Figure 11 for fail reasons by clusters). Out of 41 sensors, 12 were found to be non-significant subsystems (those referring to sensor_12 through sensor_23), and both sensor_24 and sensor_38 pressure values were found to be constant and, thus, not providing any insight about the printing process. For the remaining 25 sensors, some pairs were found to be redundant according to the clusters, and thus only one of them is considered (sensor_2-sensor_3, sensor_6-sensor_7, and sensor_26-sensor_28) for further study. The remaining 24 variables were analyzed to be following three basic profiles that can be interpreted in detail by analyzing the distribution of sensors. Figure 11: Job failure reasons. Figure 10: Job status across clusters. **Cluster 0 (non-conformable jobs):**  
The main characteristics of this cluster are as follows. Firstly, sensor_1 does not reach the recommended pressure for most of the instances and, hence, the job does not start. Sensor_3 shows a higher than expected temperature, which might result in system error. However, sensor_39 shows the measurement within specifications. Thus, the cluster should lead to unsuccessful printing. Further, the cluster is also found to contain several failed jobs with few successful ones, with the most common reasons being _failed-to-print_ and _system-error_. This aligns with our interpretation based on unsupervised analysis of the cluster data. **Cluster 1 (successful jobs):**  
This cluster is characterized as follows.