Efficient design of complex-valued neural networks with application to the classification of transient acoustic signals

A paper by the current authors Paul and Nelson [JASA Express Lett. 3(9), 094802 (2023)] showed how the singular value decomposition (SVD) of the matrix of real weights in a neural network could be used to prune the network during training. The paper presented here shows that a similar approach can be used to reduce the training time and increase the implementation efficiency of complex-valued neural networks. Such networks have potential advantages compared to their real-valued counterparts, especially when the complex representation of the data is important, which is the often case in acoustic signal processing. In comparing the performance of networks having both real and complex elements, it is demonstrated that there are some advantages to the use of complex networks in the cases considered. The paper includes a derivation of the backpropagation algorithm, in matrix form, for training a complex-valued multilayer perceptron with an arbitrary number of layers. The matrix-based analysis enables the application of the SVD to the complex weight matrices in the network. The SVD-based pruning technique is applied to the problem of the classification of transient acoustic signals. It is shown how training times can be reduced, and implementation efficiency increased, while ensuring that such signals can be classified with remarkable accuracy.