Principal Component Analysis Based Quaternion-Valued Medians for Non-Invasive Blood Glucose Estimation

For four-channel photoplethysmograms (PPGs), this paper employs quaternion-valued medians as features for performing non-invasive blood glucose estimation. However, as the PPGs are contaminated by noise, the quaternion-valued medians are also contaminated by noise. To address this issue, principal component analysis (PCA) is employed for performing the denoising. In particular, the covariance matrix of the four-channel PPGs is computed and the eigen vectors of the covariance matrix are found. Then, the quaternion-valued medians of the four-channel PPGs are found and these quaternion-valued medians are represented as the four-channel real-valued vectors. By applying the PCA to these four-channel real-valued vectors and reconstructing the denoised four-dimensional real-valued vectors, these four-dimensional real-valued vectors are denoised. Next, these denoised four-dimensional real-valued vectors are represented as the denoised quaternion-valued medians. Compared to the traditional denoising methods and the traditional feature extraction methods that are performed in the individual channels, the quaternion-valued medians and the PCA are computed via fusing all of these four-channel PPGs together. Hence, the hidden relationships among these four channels of the PPGs are exploited. Finally, the random forest is used to estimate the blood glucose levels (BGLs). Our proposed PCA-based quaternion-valued medians are compared to the median of each channel of the PPGs and other features such as the time-domain features and the frequency-domain features. Here, the effectiveness and robustness of our proposed method is demonstrated using two datasets. The computer numerical simulation results indicate that our proposed PCA-based quaternion-valued medians outperform the existing quaternion-valued medians and the other features for performing non-invasive blood glucose estimation.