Echo state network (ESN) is a powerful and efficient tool for displaying dynamic data. However, many existing ESNs have limitations for properly modeling high-dimensional data. The most important limitation of these networks is the high amount of memory consumed due to their reservoir structure and the linear output of the ESN network, which prevents the increase of reservoir units and the effective use of higher-order statistics of the features provided by its reservoir units. In this research, a new structure based on ESN is presented, in which quaternion algebra is used to compress the network data with the simple split function, and the output linear combiner is replaced by a multidimensional bilinear filter. This filter will be used for nonlinear calculations of the output layer of the ESN. In addition, the two-dimensional principal component analysis (2dPCA) technique is used to reduce the number of data transferred to the bilinear filter. In this study, the coefficients and the weights of the quaternion nonlinear ESN (QNESN) are optimized using genetic algorithm (GA). In order to prove the effectiveness of the proposed model compared to the previous methods, experiments for speech emotion recognition (SER) have been performed on EMODB dataset. Comparisons show that the proposed QNESN network performs better than the simple ESN and most currently SER systems
