# Model-Free Data Mining of Families of Rotating Machinery
## 5 Case Study
Table 1 shows the result of supervised learning using SVM. SVM shows no family structure, and all but one machines are in several classes, the resulting entropy is 0.18. Table 2 presents a square clustering to 6 classes. The resulting entropy is 0.10. Table 3 shows the clustering minimizing the _symmetric conditioned entropy_, the resulting entropy is 0.08. The harmonic feature vectors givs the desired separability, the _symmetric conditioned entropy_ separates the 6 machines better than a 6-clustering. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **0** & **1** & **2** & **3** & **4** & **5** \\ \hline M1.F1 & 18 & & & 2 & \\ \hline M2.F2 & 1 & 16 & & & \\ \hline M3.F3 & 5 & 16 & & & \\ \hline M4.F3 & 3 & & 11 & & \\ \hline M5.F4 & 2 & & & 8 & \\ \hline M6.F4 & 2 & & & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: The confusion matrix for data from six types of machines classified by SVM, to show separability. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **0** & **1** & **2** & **3** & **4** & **5** \\ \hline M1.F1 & 20 & & & & \\ \hline M2.F2 & 17 & & & & \\ \hline M3.F3 & & & 19 & 2 & & \\ \hline M4.F3 & & & 1 & 11 & 2 & \\ \hline M5.F4 & & & & 10 & \\ \hline M6.F4 & & & 2 & & 6 & 4 \\ \hline \end{tabular}
\end{table} 
Table 2: The confusion matrix for data of 6 machines 6-clustered. We also generated the dendrogram presented in Figure 4 of this data colouring recordings of machines with the same serial number with the same colour. It nicely shows the family relationship, and how well the feature vectors capture the \"characteristics\" of the machines. Since the dendrogram of the complete data set is is too large to present, we use a heat-map. For large scale clustering and family tree generation we start with all recordings we have available, the initial entropy is 6.9. Two views are presented, an overall view and a \"zoomed-in\" view of one row of the family tree. We show this in two ways: Figure 5 presents the family tree of 1800 recordings using a heat map. The recordings are on the \(x\)-axis sorted by serial number, not by family as we do not know this beforehand and the \(y\)-axis represents the clustering level. The columns of equal colour represent data clustered to the same cluster, this is raw data, no outliers removal was done besides initial z-score elimination. One can observe that there is very little fragmentation, and as we increase the number of clusters (\(y\)-axis) we move into the serial number level as can be seen by the narrow columns of equal colour. Note the \(x\)-axis (the recordings) are sorted according to the clusters here. Zooming into the second-lowest level, Table 4 gives the clustering. As this level we see large-scale family resemblances. Our industry partner, who knows all these machines by name, interpreted that at this level clustering is primarily dictated by screen size and excitation source (we anonymized the serial numbers here). We then further split a cluster, the 196, resulting in Table 5, which is at the serial number level. The machines M2.F1 and M3.F1 seem to have been changed in between the recordings, but we are not sure from the data we have. Many interesting insights into vibrating screens could be gained from this analysis. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline  & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline M1.F1 & 20 & & & & & & & & & \\ \hline M2.F2 & 17 & & & & & & & & & \\ \hline M3.F3 & & 9 & 10 & 2 & & & & & \\ \hline M4.F3 & & & & 6 & 6 & 2 & & & \\ \hline M5.F4 & & & & & & & 5 & & 5 \\ \hline M6.F4 & & 2 & & & & 4 & 4 & 2 \\ \hline \end{tabular}
\end{table} 
Table 3: The confusion matrix for data from six types of machines clustered into ten clusters as determined by optimizing the _symmetric conditioned entropy_. Figure 4: Dendrogram, same 6 machines as in Figure 3, colour indicates machine.