# Bearing Health Monitoring Using Relief-F-Based Feature Relevance Analysis and HMM
## 4 Results and Discussion
It is worth noting to mention that the inclusion of a suitable feature selection approach increases the accuracy of the HMM-based classifier adopting a few numbers of relevant features (interpretable measures). At the same time, it helps to get a better \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **\# Feat.** & **Best Acc. (\%)** & **Best \# Feat.** & **Acc (\%)** \\ \hline No feature selection & 53 & \(96.97\pm 0.83\) & - & - \\ VRA & 53 & \(96.92\pm 0.84\) & 51 & \(95.63\pm 1.07\) \\ Self-weight & 53 & \(96.69\pm 0.76\) & 41 & \(95.17\pm 1.06\) \\ Laplacian Score & 37 & \(97.28\pm 0.92\) & 33 & \(95.87\pm 0.79\) \\ Distance-weight & 15 & \(99.74\pm 0.29\) & 13 & \(99.36\pm 0.39\) \\ SFS & 11 & \(99.94\pm 0.12\) & 9 & \(99.56\pm 0.40\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Best classification results and number of features required (four class problem). Figure 4: The learning curve results are shown for the feature rankers studied using an hidden Markov models (HMM) classifier. We present the average of the testing set performance under a nested 10-fold cross-validation strategy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **\# Feat.** & **Best Acc. (\%)** & **Best \# Feat.** & **Acc (\%)** \\ \hline No feature selection & 53 & \(98.97\pm 0.46\) & - & - \\ VRA & 51 & \(99.01\pm 0.42\) & 47 & \(98.47\pm 0.58\) \\ Self-weight & 43 & \(99.39\pm 0.43\) & 37 & \(98.84\pm 0.62\) \\ Laplacian Score & 43 & \(99.53\pm 0.33\) & 33 & \(98.80\pm 0.49\) \\ Distance-weight & 11 & \(99.95\pm 0.07\) & 7 & \(99.76\pm 0.11\) \\ SFS & 11 & \(99.91\pm 0.16\) & 7 & \(99.74\pm 0.21\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Best classification results and number of features required (ten class problem). representation space for visualizing the data distribution. In this sense, Figure 6 shows a 2D and 3D data projection based on the centered kernel alignment (CKA) algorithm applied to the relevant features computed by our SFS approach. CKA projects the original domain's data into rotated points of lower dimensionality space, evaluating the similarity between an input kernel matrix (given by the relevant features set) and a target kernel computed over the output labels [70]. As seen, the separability between N and failure states are clear; additionally, the representation displays overlapping between samples belonging to the B, IR, and OR classes, as before corroborated by the confusion matrices and by other state-of-the-art approaches [71]. Table 6 presents a comparative study of the achieved SFS results and state-of-art approaches devoted to bearing fault diagnosis and its evaluation. Here, two main aspects are deemed: (i) the method has to be proven on the Western Case University database, and (ii) the metric used to evaluate the diagnosis/evaluation performance has to be the classification accuracy. It is possible to observe that the proposed SFS approach outperforms the majority of the studied methodologies concerning the trade-off between classification accuracy and the required number of features. Additionally, note that a significant amount of methods do not include a feature selection stage. Still, at the expense of lower classification accuracy [22; 27; 72; 73; 74]. On the other hand, methodologies that incorporate feature selection techniques demonstrate better discrimination results [44; 46; 47; 74; 75]. In particular, two proposals stand out: the work presented by [PERSON] et al. in [25] and our SFS-based approach. Although the first one uses the smallest number of features, the experimental results reported in the paper were calculated using a simple validation framework. They employed only 174 samples (24 per class) to generate two subsets of data (84 samples for training and 90 for testing). Besides, our methodology can identify both the bearing state and the severity level of all the fault listed in the database; meanwhile, the work presented in [25; 76] only considers six classes.