# Dempster-Shafer Fusion Based on a Deep Boltzmann Machine for Blood Pressure Estimation
## 4 Experimental Results and Statistical Analysis  
To implement this work, the 15 feature vectors acquired from the OMWs and OMW envelopes [12] were used as summarized in [12]. We selected the number of BP categories as \(K\)(=10) to build a sophisticated classifier for SBP and DBP, respectively, as shown in Table 1. To classify SBP and DBP target values determined by the nurses, we used the \(k\)-medoids algorithm in Matlab(r) 2017. The \(k\)-medoids method imposed a clustering structure on the SBP and DBP target values.Therefore, we obtained the \(k\) cluster medoid locations as shown in the second and third columns of Table 1.  
The algorithm is renowned as as being real-valued and less sensitive to the presence of noise compared to \(k\)-means [18]. We conducted training and testing experiments to evaluate DBM-based DS fusion technology. The subjects' BP measurements were sequentially divided into training data (340 sets from 68 subjects) and test sets (85 sets from 17 subjects). Indeed, the five measurements obtained from the individual subjects is a very a small number for the input data in the deep learning. Thus, we adopted the artificial data acquired using the real data. We used the unseen real data to evaluate the new technique in the test step. We increased the epoch number from 10 to 100. As a result of the experiment, the mean square error (MSE) was rapidly decreased until 20 epochs. From that point, it was slightly increased and decreased until 100 epochs. We then tuned the performance of the proposed method on the identical conditions with a different number of hidden units from 16 up to 128 owing to the dimension \(\mathbb{R}\)(=15) of the input features. The best benefit of the proposed method was found at 64 hidden units, which showed that a small number of hidden units could cause a higher mean absolute error (MAE) and standard deviation of error on account of underfitting, whereas a large number of hidden units could lead to an increased MAE and SDE because of overfitting. Next, we chose the number of hidden units (=64) and number of epochs (=100) to compare the running time between the DBM-based DS fusion and DBM techniques. We summarized the input order of the new technique as 15, the output order as 20, and the hidden unit as 2. The total of the training and test times was calculated based on Matlab(r) 2017 [26]. It was adequately short for real BP application because it processed 8500 pieces of data in 6130.8 s. From this result, the DBM-based DS fusion called for a higher complexity time than the DBM technique, which was owing to the fusion process. For comparison, we first investigated the accuracy of the BP classifiers using a support vector machine (SVM), SVM with DS fusion (SVMDS), DBN, DBN with DS fusion (DBNDS), DBM, and proposed DBM-based DS fusion (DBMDS), as presented in Table 2. We found that BP classification probability (sensitivity) versus false alarm probability (1-specificity) across varying cut-off produces a receiver operating characteristic (ROC) curve in the square as shown in Figure 4. The characteristic of the ROC curve gradually shows better performance nearer to the upper left. Therefore, the fusion SBP and DBP estimators have a better performance than the single SBP and DBP estimators. The new fusion scheme for SBP and DBP measurements was evaluated by the mean error (ME) and SDE between the estimated BP categories obtained from the classifier and target BP categories in accordance with the recommendations of the American National Standards Institute (ANSI)/American Association of Medical Instruments (AAMI) standard protocol [19], as shown in Table 3. BP devices are evaluated as passing on a standard protocol [19] basis if the ME is less than 5 mm Hg and the SDE is less than 8 mm Hg versus the reference. Additionally, the British Hypertension Society (BHS) protocol determines the achievement of BP estimates with a cumulative percentage of readings belonging to the mean absolute errors of 5 mmHg, 10 mmHg and 15 mmHg in stethoscope measurements of two trained