This paper proposes a novel method to detect anomalies in large datasets under a fully unsupervised setting. The key idea behind our algorithm is to learn the representation underlying normal data. To this end, we leverage the latest clustering technique suitable for handling high dimensional data. This hypothesis provides a reliable starting point for normal data selection. We train an autoencoder from the normal data subset, and iterate between hypothesizing normal candidate subset based on clustering and representation learning. The reconstruction error from the learned autoencoder serves as a scoring function to assess the normality of the data. Experimental results on several public benchmark datasets show that the proposed method outperforms state-of-the-art unsupervised techniques and is comparable to semi-supervised techniques in most cases.
In the article, the authors solve the problem of anomaly detection using a fully unsupervised approach. They try to deal with the main challenge of anomaly detection: a lack of certainty on what defines normal data and anomaly one. For this purpose, the authors iteratively use: 1) autoencoders to learn the representation of the data; 2) applying in the latent space clustering to get a new training set and retrain autoencoders. The experimental results show that the author’s method performed better results than such a baseline model as one-class SVM and one-class NN. 
 
The proposed algorithm looks robust and well-motivated, but the text of the article and the experiments can be improved. As the proposed approach is a heuristic, the experiments should be done more persuasively, including more metrics used and more alternative algorithms considered. 
The key comments are the following:
1. The formatting of the article needs to be improved e.g.:
2. there is no comma between rows in the equation (1) ;
<<to be accepted into the “training” set, .>> - there is an extra comma;
3. round brackets in the equation (6) should be bigger;
4. Table 3 is bigger than the page sizes.
5. The quality of the pictures should be improved:
- Increase the captions font size in Figure 2;
- The captions and the legends in Figure 3 are practically not visible;
6.  Is the DAGMM method SOTA in anomaly detection with deep autoencoder? There are many other methods with similar ideas. We expect that we should provide a comparison with other methods: 
https://arxiv.org/pdf/1809.02728.pdf - IGMM-GAN
https://papers.nips.cc/paper/7915-generative-probabilistic-novelty-detection-with-adversarial-autoencoders.pdf - GPND AE
6. Also, DAGMM works badly according to the experiments in the article with max AUROC in Table 1 only 50.3 (so it seems that it is no better than the coin-flipping)
7. Why was the only selected digit for analysis 4? Usual for comparison anomaly detection on MNIST dataset apply the following procedure: for each figure in dataset consider corresponded class as anomaly data, and the rest of the digits are used as normal data, e.g.:
https://arxiv.org/pdf/1802.06222.pdf
https://arxiv.org/pdf/1906.11632.pdf 
8.  Class imbalances can affect the value of the AUROC metric. Possibly, the other metrics like AUPRC, F1-scores will better reflect the work of the algorithms for comparison. Also, AUROC is not representative when it comes to the selection of the threshold for anomaly detection. Precision and Recall can help to get more insights.
9. In Table 3, the result of applying the proposed algorithm presented with standard deviation, but other methods are represented by one metric value. Why? The explanation is required.