MATRIX ANALYSIS OF NEURAL NETWORK ARCHITECTURES FOR AUDIO SIGNAL CLASSIFICATION
MATRIX ANALYSIS OF NEURAL NETWORK ARCHITECTURES FOR AUDIO SIGNAL CLASSIFICATION
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DOI：
10.25144/13374
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
V. Paul;P. Nelson
中科院分区：
文献类型：
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作者：
V. Paul;P. Nelson
鉴于在音频信号处理中越来越多地使用神经网络来完成各种任务，本文首先对一般网络结构的前向和后向传播进行了严格的分析。本文以多层感知器(MLP)为研究对象，利用矢量化前向传播的基本原理，推导出具有任意隐含层的MLP模型的一般反向传播方程。在应用链式规则的导数时，使用了矩阵微积分的规则，并定义了向量和矩阵形式的简化方程，以计算误差相对于网络权重的梯度。通过使用诸如音频频谱分类之类的信号处理任务的例子，进一步研究了所导出的方程。将奇异值分解(SVD)应用于权值矩阵，以帮助理解网络行为。
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.