Matrix analysis of neural network architectures for audio signal classification

Paul, Vlad Stefan and Nelson, Philip (2020) Matrix analysis of neural network architectures for audio signal classification. In Proceedings of the Institute of Acoustics. vol. 42, Institute of Acoustics..

Record type: Conference or Workshop Item (Paper)

Abstract

Given the increased use of neural networks for various tasks in audio signal processing, this paper concentrates firstly on providing a rigorous analysis of forward and backward propagation for general network architectures. This paper concentrates on the Multi-layer Perceptron (MLP) and use the basic vectorized forward propagation to derive general backpropagation equations for an MLP model with any number of hidden layers. The rules of matrix calculus are used when applying the derivatives for the chain rule and simplified equations in vector and matrix form are defined for the computation of the gradients of the error with respect to the weights of the network. The equations derived are investigated further by using examples of signal processing tasks such as the classification of audio spectra. The singular value decomposition (SVD) is applied to the weight matrices to help understand the network behaviour.

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