Speech Emotion Recognition System by Quaternion Nonlinear Echo State\n Network

The echo state network (ESN) is a powerful and efficient tool for displaying\ndynamic data. However, many existing ESNs have limitations for properly\nmodeling high-dimensional data. The most important limitation of these networks\nis the high memory consumption due to their reservoir structure, which has\nprevented the increase of reservoir units and the maximum use of special\ncapabilities of this type of network. One way to solve this problem is to use\nquaternion algebra. Because quaternions have four different dimensions,\nhigh-dimensional data are easily represented and, using Hamilton\nmultiplication, with fewer parameters than real numbers, make external\nrelations between the multidimensional features easier. In addition to the\nmemory problem in the ESN network, the linear output of the ESN network poses\nan indescribable limit to its processing capacity, as it cannot effectively\nutilize higher-order statistics of features provided by the nonlinear dynamics\nof reservoir neurons. In this research, a new structure based on ESN is\npresented, in which quaternion algebra is used to compress the network data\nwith the simple split function, and the output linear combiner is replaced by a\nmultidimensional bilinear filter. This filter will be used for nonlinear\ncalculations of the output layer of the ESN. In addition, the two-dimensional\nprincipal component analysis technique is used to reduce the number of data\ntransferred to the bilinear filter. In this study, the coefficients and the\nweights of the quaternion nonlinear ESN (QNESN) are optimized using the genetic\nalgorithm. In order to prove the effectiveness of the proposed model compared\nto the previous methods, experiments for speech emotion recognition have been\nperformed on EMODB, SAVEE, and IEMOCAP speech emotional datasets. Comparisons\nshow that the proposed QNESN network performs better than the ESN and most\ncurrently SER systems.\n