# Dempster-Shafer Fusion Based on a Deep Boltzmann Machine for Blood Pressure Estimation
## 1 Introduction  
Most medical offices, hospitals, and home monitoring devices use an oscillometric technique to measure blood pressure (BP) because maintaining a healthy BP is critical to living a long healthy life. The algorithm of maximum amplitude (MAA) is predominantly utilized to estimate the BP mean by monitoring the cuff pressure in the maximum oscillation. However, the MAA using a fixed ratio is insufficient for estimating the BP since the proportion of these fixed characteristics significantly varies according to the rhythm of the heart, movement artifacts, and cuff size [1, 2], which leads to uncertainties of the BP in practice in the oscillometric BP measurements [3, 4, 5]. Physiological characteristics have a significant impact on these ratios. Recently, [PERSON] et al. [6] studied a method using electrocardiogram (ECG) signals for BP estimation. A simple cuffless technique based on ECG using machine learning was developed by [PERSON] et al. [7]. Meanwhile, neural networks (NNs) have been presented to address the fixed ratio problem of using the MAA technique, which does not employ mathematically complicated models [8]. To estimate BP, the NNs can be more robust methods than the mathematical models in terms of artifacts and noise [8]. An NN with a feature-based technique employing a back-propagation algorithm was thus devised [9]. The Gaussian mixture regression (GMR) and improved GMR were further proposed by [PERSON] et al. to estimate BP [4, 5]. In recent years, a deep learning technique has emerged as an outstanding trend in machine learning for signal processing areas. [PERSON] et al. [10] introduced a method based on deep learning [11] to estimate the BP when only a small sample is available. However, this technique has limitations owing to the input BP data consisting of only five BP sample sets per individual volunteer, which acts as an obstacle when using the deep belief network (DBN) technique. The small number of data cannot ensure desirable identification of the DBN to use the complex nonlinearmodel. This critical limitation leads to various problems, such as overfitting, since the DBN comprises the complex nonlinear model, including many layers, parameters, and weights. This problem was addressed by increasing the size of the input data by utilizing the parameter bootstrap scheme [12]. Furthermore, a deep Boltzmann machine (DBM) regression model [13] was recently proposed by [PERSON] et al. [12] to resolve the uncertainty. However, the DBN and DBM models can also cause estimate uncertainties in cases in which many random initialized parameters and functions remain. Motivated by these issues, a DBM-based [12; 13] Dempster-Shafer (DS) fusion [12; 14] technique is herein presented to classify and estimate the SBP and DBP categories without characteristic ratios. DBM is an advanced technology of the accumulation of restricted Boltzmann machines (RBMs) [13]. Unlike DBN [13], each unit in the middle layer of the DBM acquires signal up and down to prevent uncertainty at the inference step [12]. More recently, the concepts of fusion and ensemble were employed in BP estimation to increase the performance of BP measurements [15; 16; 17]. DS fusion enables the evidence uncertainty to have upper and lower bounds that can be incorporated as a method for combined independent estimation of the observations, while also enabling the clear achievement and increased confidence in a given DBM estimate [16]. Consequently, we provide an accurate BP category and a methodology that can reduce the estimation uncertainty. Specifically, this research provides the following contributions and improvements over that presented in [10; 12]:  
* A methodology to acquire BP estimates utilizing oscillometric BP data is provided, and a BP category using DBM-based DS fusion [14; 15] is presented. * The DS combination is comprised of fused independent estimations of the observations.