A Hybrid Echo State Network for Hypercomplex Pattern Recognition, Classification, and Big Data Analysis

Processing big data with high-dimensional forms is one the most challenging parts of analyzing different signals and systems for various applications, including decision-making, pattern recognition, classification, etc. This procedure can be more problematic when interpreting and modeling complex phenomena. On the other hand, the processing speed in machine learning (ML) methods may not be acceptable, especially for real-time implementations. In other words, the more accurate a signal is, the more latency can occur. Recently, echo state networks (ESN) have shown appropriate precession in signal processing and classifying variables. However, utilization of a reservoir layer affects their speed, particularly for high-dimensional data. This paper presents a powerful ESN method for pattern recognition and classification of complex phenomena based on a new octonion ESN called octonion nonlinear ESN (ONESN). This method includes a modified version of the conventional ESN, in which all computations from the real space are mapped to the octonion space. Consequently, the size of the reservoir and its weights are reduced to 1/8 of its initial amount, increasing the speed of processing. Also, a bilinear filter to improve the performance of the conventional ESN is added to the output of the network.