Construction of dictionaries using nonnegative matrix factorisation (NMF) has extensive applications in signal processing and machine learning. With the advances in deep learning, training compact and robust dictionaries using deep neural networks, i.e., dictionaries of deep features, has been proposed. In this study, we propose a probabilistic generative model which employs a variational autoencoder (VAE) to perform nonnegative dictionary learning. In contrast to the existing VAE models, we cast the model under a statistical framework with latent variables obeying a Gamma distribution and design a new loss function to guarantee the nonnegative dictionaries. We adopt an acceptance-rejection sampling reparameterization trick to update the latent variables iteratively. We apply the dictionaries learned from VAE-NMF to two signal processing tasks, i.e., enhancement of speech and extraction of muscle synergies. Experimental results demonstrate that VAE-NMF performs better in learning the latent nonnegative dictionaries in comparison with state-of-the-art methods.

翻译：利用非负矩阵因子化(NMF)构建词典在信号处理和机器学习方面有着广泛的应用。随着深神经网络(即深特征词典)在深神经网络(即深特征词典)的深学习、培训紧凑和稳健词典方面的进步,我们提出了使用非负矩阵因子化(NMF)进行非负矩阵学习的概率基因化模型。与现有的VAE模型相比,我们将该模型置于一个统计框架之下,其中含有符合伽玛分布的潜伏变量,并设计了一个新的损失函数,以保障非负词典。我们采用了接受-拒绝采样重新校准技巧,以迭代方式更新潜在变量。我们从VAE-NMF学的词典用于两个信号处理任务,即加强言词和提取肌肉协同作用。实验结果表明,VAE-NMF在学习潜在非负词典方面比国家艺术方法要好。