The Adversarially Learned Mixture Model (AMM) is a generative model for unsupervised or semi-supervised data clustering. The AMM is the first adversarially optimized method to model the conditional dependence between inferred continuous and categorical latent variables. Experiments on the MNIST and SVHN datasets show that the AMM allows for semantic separation of complex data when little or no labeled data is available. The AMM achieves unsupervised clustering error rates of 3.32% and 20.4% on the MNIST and SVHN datasets, respectively. A semi-supervised extension of the AMM achieves a classification error rate of 5.60% on the SVHN dataset.
The paper presents a method for un-/semi- supervised clustering which combines adversarial learning and Mixture of Gaussian. 
Cons:
It is interesting to incorporate the generative model into GAN.
Probs:
1.	The author claims the method is the first one to generative model inferring both continuous and categorical latent variables. I think that such a conclusion is overclaimed, there are a lot of related works, e.g., Variational deep embedding: An unsupervised generative approach to Clustering, IJCAI17; Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks, ICML2017. Multi-Modal Generative Adversarial Networks for Diverse Datasets, ICLR19 submission. In fact, these methods are also very competitive approaches to clustering. 
2.	Is adversarial learning do helpful for clustering with the generative model? Some theoretical should be given, at least, some specified experiments should be designed.  
3.	The novelty should be further summarized by highlighting the difference with most related works including but not limited the aforementioned ones. The current manuscript makes the work seem like a straightforward combination of many existing approaches. 
4.	In fact, the paper is hard to follow. I would recommend improving the logic/clarity.