For the four channel photoplethysmograms (PPGs), this paper proposes a quaternion valued based method for performing the non-invasive blood glucose estimation. First, these four channel PPGs form a quaternion valued signal. Then, the quaternion valued means and the quaternion valued medians of this quaternion valued PPGs are employed as features. Next, the quaternion valued long short term memory (QLSTM) based recurrent neural network (RNN) is employed for estimating the non-invasive blood glucose values. Unlike the traditional methods based on extracting the features in each channel of the PPGs independently and fusing all the features together in the conventional neural networks, the quaternion valued operations performed on the quaternion valued PPGs only fuse the same features among these four channels together while do not fuse different features among these four channels together. Hence, the physical interpretations of the features preserve. To demonstrate the effectiveness and the robustness of our proposed method, two datasets are evaluated. The computer numerical simulation results show that our proposed method can yield 81.43% and 83.09% of the test data falling in the zone A of the Clark error grid for the test data in the first dataset and in the second dataset, respectively. Also, it can yield the mean absolute relative difference (MARD) at 14.41% and 14.31% for the test data in the first dataset and the second dataset, respectively. This demonstrates the superior performance of our proposed method over the existing methods for the test data in the both datasets.
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