We study a variant of the variational autoencoder model (VAE) with a Gaussian
mixture as a prior distribution, with the goal of performing unsupervised
clustering through deep generative models. We observe that the known problem of
over-regularisation that has been shown to arise in regular VAEs also manifests
itself in our model and leads to cluster degeneracy. We show that a heuristic
called minimum information constraint that has been shown to mitigate this
effect in VAEs can also be applied to improve unsupervised clustering
performance with our model. Furthermore we analyse the effect of this heuristic
and provide an intuition of the various processes with the help of
visualizations. Finally, we demonstrate the performance of our model on
synthetic data, MNIST and SVHN, showing that the obtained clusters are
distinct, interpretable and result in achieving competitive performance on
unsupervised clustering to the state-of-the-art results.

我们研究了一个变分自编码器模型（VAE）的变体，其中高斯混合作为先验分布，通过深生成模型实现无监督聚类，通过最小信息约束启发式，缓解了过度正则化问题，并在合成数据、MNIST 和 SVHN 上证明了模型的性能。