Augmented Online Sequential Quaternion Extreme Learning Machine

Online sequential extreme learning machine (OS-ELM) is one of the most popular real-time learning strategy for feedforward neural networks with single hidden layer due to its fast learning speed and excellent generalization ability. When dealing with quaternion signals, traditional real-valued learning models usually provide only suboptimal solutions compared with their quaternion-valued counterparts. However, online sequential quaternion extreme learning machine (OS-QELM) model is still lacking in literature. To fill this gap, this paper aims to establish a framework for the derivation and the design of OS-QELM. Specifically, we first derive a standard OS-QELM, and then propose two augmented OS-QELM models which can capture the complete second-order statistics of noncircular quaternion signals. The corresponding regularized models and two approaches to reducing the computational complexity are also derived and discussed respectively. Benefiting from the quaternion algebra and the augmented structure, the proposed models exhibit superiority over OS-ELM in simulation results on several benchmark quaternion regression problems and colour face recognition problems.