  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.
