From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Submission Withdrawn by the Authors

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_89gj
title: Clarification is satisfied. 
comment: Thanks for the clarification. My concern is resolved, and I have raised my score.

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to concerns of Reviewer 89gj
comment: Thank you for your comments below as we respond in line.

"The author provide the contribution of the methods that are specially designed for tabular data. However, it is hard to understand how these methodologies contribution are related to tabular data. For example, why independent target distribution works better for tabular data than t-distribution?"
 
1. Because the independent target distribution is set to **multivariate Gaussian distribution to better capture the distribution of multivariate tabular data**. Otherwise, the same t-distributed embedding and its derivative are proposed for learning image representation. We showed in the Table (Appendix A) to explain why such t-distribution embedding, borrowed from the data visualization embedding, is different from the requirements for the embedding required for clustering 

"Does it also work better for other data types?" 

2. No, this method is not expected to work on image data because multivariate Gaussian distribution of such high-dimensional data is not practical. A majority of tabular data in the UCI repository are of lower dimensions compared to popular benchmark image data sets. Because we see deep learning through the lens of computer vision/image based problems, the same conclusions or benchmark cannot be recommended for text, tabular, graph-related data structures. 

"And why fully-connected Autoencoders work better for tabular data than convolutional counterparts?"

3. We explained this extensively in our previous response and in the manuscript that **heterogeneous tabular data DO NOT contain the spatial regularity as image data**. The convolution operation between filter kernels and the data requires spatial or temporal regularity in homogeneous data (variations in images and signals). **In contrast, tabular data are heterogeneous without such regularity, which makes convolution-based filtering ineffective for feature extraction.** Considering CNN as the optimal solution for all data problems without understanding the data (text, tabular, graph) would keep surprising us with unexpected results, unfortunately.

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_89gj
title: Still not clear about the specified operations towards tabular
comment: The author provide the contribution of the methods that are specially designed for tabular data. However, it is hard to understand how these methodologies contribution are related to tabular data. For example, why independent target distribution works better for tabular data than t-distribution? Does it also work better for other data types? And why fully-connected Autoencoders work better for tabular data than convolutional counterparts?

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to Reviewer wyoM
comment: Thank you for your comments.

"I still believe that setting the target distribution P through clustering in the input space provides no clear advantage. This is illustrated in the experimental results: although G-CEALS is a complicated procedure, it does not provide significant better results compared to simple GMM or k-means." 
1. If we **completely ignore** the context and challenge of learning heterogeneous **tabular data**, the comparison results with GMM and K-means would appear **misleadingly trivial**. While significant inference is a statistical consideration, consistently top-rank ordering of G-CEALS (Table 3) across **eight multi-domain "tabular data sets"** puts much confidence in the advantage of considering the P space. 

"Note also that G-CEALS includes a hyperparameter gamma that is tuned using the ground truth labels, while ground truth information is not exploited in k-means or GMM. "

2. We agree. That's why beating these traditional machine learning methods on **tabular data is still quite challenging**. The deep tabular learning literature is still struggling to beat fast and simple traditional machine learning models, even using very complex and deep architectures. 

"I am not convinced that G-CEALS is an effective method that deserves to be used for clustering tabular data providing a clear advantage over typical clustering algorithms."

3. **Again, the G-CEALS method is NOT a clustering method**. It is a method to obtain a quality embedding that can be used in downstream classification or clustering. Joint clustering improves embedding learning, which can be replaced by joint classification methods.

"As mentioned in my review, I am against the use of ground truth labels for setting hyperparameters in clustering. "

4. **Again, the hyperparameters were NOT used in clustering**. It was used in learning the embedding via an autoencoder where the contribution of cluster distribution to embedding learning was balanced using the gamma parameter, as it is done in all existing studies in the cluster embedding literature. We did not make any exceptions to that common practice.

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_wyoM
title: Response to rebuttal
comment: I still believe that setting the target distribution P through clustering in the input space provides no clear advantage. This is illustrated in the experimental results: although G-CEALS is a complicated procedure, it does not provide significant better results compared to simple GMM or k-means. Note also that G-CEALS includes a hyperparameter \gamma that is tuned using the ground truth labels, while ground truth information is not exploited in k-means or GMM.  I am not convinced that G-CEALS is an effective method that deserves to be used for clustering tabular data providing clear advantage over typical clustering algorithms.
As mentioned in my review, I am against the use of ground truth labels for setting hyperparameters in clustering. In addition to that, it can be observed from table 6 that the selected values of \gamma vary considerably across the folds indicating that the method is very sensitive on \gamma.

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to Reviewer 3YZr
comment: Thank you for your response. 

GMM and k-means are one of the simplest traditional clustering algorithms. Outperforming them does not say too much about the performance of the method. I suggest using stronger classical baselines.

1. A careful reading of the deep tabular data learning literature (as cited above) should clarify why GMM and K-means remain stronger baselines for tabular data. Our results confirm that FC and CNN-based embeddings do not outperform simple clustering of input data unless treated with a data-specific learning algorithm like ours. Regrettably, this data-specific problem is often confused with some of the stringent notions drawn from the computer vision domain. 

The authors added CNN architectures to the comparison, which is not what I asked for. I only meant that we could replace the CNN layers with FC layers in many SOTA models, which were run on image data. Running CNN architectures is misleading.

2. We provided details in Appendix B on why converting deep CNN to FC is not sufficient for tabular data to make a fair comparison. Transfer learning, image filtering, image augmentations - many steps in image learning cannot be reproduced for tabular data. 

Many authors run their model on e.g. MNIST interpreted as tabular data (ignoring the image structure) using FC networks. It would then be easier to compare with other methods. 

3. Converting MNIST to tabular does not make it tabular by definition (Preliminaries: Section 3.1). MNIST data tables would still contain homogenous and high-dimensional pixels in vectors, unlike heterogeneous vectors in tables. Ideally, we should not be using "image-like" data to show the superiority of deep models, which is a well-established fact.  

The authors should also extend the comparison and run the model on more number and more diverse datasets. Most datasets are small and low dimensional.

4. Tabular data sets are widely available in low dimensions and low sample sizes if we take a closer look at the UCI data repository. The superiority of deep learning has already been shown for large sample sizes and dimensions. This algorithm is particularly designed for learning more challenging (low-dimensional and low-sample size) heterogeneous data problems, not for learning diverse image-based or high-dimensional data.

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_3YZr
title: Response to Authors' rebuttal 
comment: GMM and k-means are one of the simplest traditional clustering algorithms. Outperforming them does not say too much about the performance of the method. I suggest using stronger classical baselines.

The authors added CNN architectures to the comparison which is not what I asked for. I only meant that we could replace the CNN layers with FC layers in many SOTA models which were run on image data. Running CNN architectures is misleading.

Many authors run their model on e.g. MNIST interpreted as tabular data (ignoring the image structure) using FC networks. It would be then easier to compare with other methods. The authors should also extend the comparison and run the model on more number and more diverse datasets. Most datasets are small and low dimensional. 

Taking the aforementioned issues into account I cannot recommend the acceptance.

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to Reviewer 
comment: We appreciate your valuable feedback and the opportunity to update relevant sections (5.2, 6.1, 7.1, 7.2) to clarify the concerns below. The key point is that the optimal methods for learning multivariate tabular data are different from those adopted for image learning, as evidenced in our results and the literature.  

Weakness 1 

Indeed, clustering on high-dimensional image pixel space is ineffective. However, traditional machine learning methods still perform strongly on tabular data compared to deep learning methods (Kadra et al. 2021, Borisov et al. 2021, Kohler et al. 2019, Smith et al. 2020, Shwartz-Ziv & Armon, 2022). Our results confirm that clustering accuracy on the latent space (Z) is worse than clustering on tabular data space (Tables 2 and 3). Therefore, the superior cluster distribution (on tabular data space) is chosen as the target distribution to complement the shortcomings of the autoencoder embedding in this data context (Eq. 7). 

Weakness 2 

We have updated Section 5.1 to clarify this concern. All cluster-embedding methods in the literature use this crucial trade-off parameter (gamma) to balance the contribution of two competing losses: 1) encoder reconstruction loss and 2) clustering loss. The final embedding quality is then evaluated in downstream clustering using ACC and NMI metrics that require ground truth labels. Although these metrics (and ground truth) are never involved in training, the gamma hyperparameter is tuned via grid search on ACC or NMI metric for model selection and reproducibility, as in other studies (IDEC, DKM). In this regard, Fard et al. state, "While one might argue that such procedure affects the unsupervised nature of the clustering approaches, we believe that a clear and transparent hyperparameter selection methodology is preferable to a vague or hidden one." Although clustering is performed on the entire data set in prior studies, we trained our model on a training data split to show the reproducible quality of embedding on unseen test data. 

Weakness 3 

Indeed, GMM and K-means are the worst clustering methods on image pixel space. Therefore, a new cluster-embedding method is expected to outperform these basic clustering methods significantly. In contrast to this notion, traditional machine learning still outperforms deep learning on tabular data, as mentioned in our response to weakness 1.  So, GMM and K-means are competitive clustering methods for tabular data, as evident in Tables 2 and 3 (ranked 3rd), where baseline cluster embedding methods (DEC, clustering on Z, DKM, CNN) struggled to outperform GMM and K-means. Unlike image learning, it still remains a challenge for any deep representation of tabular data to outperform traditional machine learning, supported by the conclusion “tabular data sets are the last unconquered castle for deep learning” (Kadra et al. 2021). Consequently, the challenge is to yield a robust representation of tabular data that can significantly outperform traditional clustering methods. 

Several concerns:

Source code is not available: We included a footnote on page 5 that the source code will be publicly shared following the double-blind review sessions. The GitHub URL is kept hidden for anonymity as required by ICLR policy.

1.	Following our responses to weaknesses 1 and 3, it is obvious why the proposed idea on tabular data is opposite to the general understanding of image learning. Therefore, the superior cluster distribution is set as the target distribution to complement the quality of autoencoder embedding.  Our proposed embedding outperforms both autoencoder embedding (Z) and traditional clustering (GMM, K-means).  

2.	Thanks! We have updated the algorithm as suggested.

3.	We replaced Cluster (X) with “K-means or GMM clustering of X” on line 3 of the algorithm.

4.	We do not have a pre-defined convergence criterion for the algorithm. Instead, all methods were trained for 5000 epochs in search of the best model to reproduce a quality embedding on test data (Section 6.1). Table 6 (Appendix D) shows the number of epochs required for each training fold. 

5.	The sensitivity of the hyperparameter is discussed in our response to weakness 2 above and in revised Sections 5.2, 7.2, 7.3, and Table 6 (Appendix D).

6.	The ClusterGAN method converted the RNA sequence 10x73k data set into a count matrix in a 2D tabular grid. The penDigits is a time-series data represented in a 2D (x, y) coordinate. In contrast, standard tabular data consist of heterogeneous variables (e.g., age, salary, height, weight) and multivariate distributions of a feature vector. While time-series data can be represented in tables, they need special architectures to learn temporal patterns, which we do not consider in this study. We provide preliminaries on tabular data in Section 3.1 and a discussion (Section 7.1 – Image versus tabular data embedding) to draw a contrast between image and tabular data.

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to Reviewer 
comment: We appreciate your valuable feedback and the opportunity to update relevant sections (2.1, 3.1, 3.2, 3.3, 4.1, 5.1), Appendix B, and Tables 2, 3, and 5 to clarify the concerns below.  The key point is that the optimal methods for learning multivariate tabular data are different from those adopted for image learning, as evidenced in our results.   

1. Concerning deep learning baselines: There is mounting evidence that traditional machine learning still outperforms deep learning on tabular data (Kadra et al. 2021, Borisov et al. 2021, Kohler et al. 2019, Smith et al. 2020, Shwartz-Ziv & Armon, 2022), asserting “tabular data sets are the last unconquered castle for deep learning”. A robust representation learning of tabular data is still challenging and rarely explored as extensively as image and text data. While CNN is effective for data with spatial regularity (images) or temporal regularity (time-series), tabular data with heterogeneous variables are often devoid of such regularity.   Therefore, it is not surprising that K-means/GMM clustering of tabular data can be superior to clustering on a latent space (Tables 2 and 3). Therefore, traditional clustering methods are still competitive baselines for tabular data in the absence of robust representation learning baselines.  

2. Concerning single-layer autoencoder: We now compare cluster embedding results of convolutional autoencoders (CNN-AE) and fully connected autoencoders (FC-AE) for single-layer and three-layer settings in Table 5 (Appendix C). Table 5 shows that single layer and FC-AE architectures on tabular data are superior to deep or CNN architectures. Table 3 shows that the CNN autoencoder ranks 4th and is worse than GMM/K-means clustering of tabular data.  

3. Concerning upgrade/downgrade of existing models: Many approaches (e.g., transfer learning, image augmentation) used in image learning are not trivial on tabular data. Therefore, learning architectures proposed for images are not directly applicable to feature vectors in data tables. To avoid architectural bias and ensure a fair comparison of the algorithms, we use a single-layer architecture.  For example, the latent dimension (256) in image learning methods would result in an overcomplete architecture for tabular data (input:7, latent:256). Unfortunately, there is no standard benchmark for tabular data like MNIST or CIFAR and no prior cluster embedding study on tabular data. So, we select a common latent dimension (5) considering the range of input dimensionality (7 to 241, Table 1). Similarly, 2D CNN architecture needs to be downgraded to 1D to convolve with tabular feature vectors. Our contribution is not to upgrade the learning architecture (e.g., adversarial, stacked, convolutional, deep) to beat the state-of-the-art performance on existing benchmarks but to make a fair comparison across algorithms on tabular data for which the benchmark is expected to change.  

4. Concerning the exclusion of some methods: We have updated Section 5.1 (Baseline methods) and included results from several existing methods (DKM, CNN-GMM, CNN-K-means) in Tables 2, 3, and 5. In Appendix B, we detail five existing methods (DeepCluster, DEPICT, DKM, DCN, DynAE) to explain why tabular data cluster embedding is not directly reproducible without customizing. As an example, we use the original DKM model to reproduce cluster embeddings on tabular data (Table 2), which performs far worse than other baselines (Table 3). 

5. Concerning if improving ACC or NMI is the main goal of the clustering: We are proposing an algorithm to obtain a quality embedding for tabular data that can be used in downstream classification and clustering tasks. ACC and NMI are the most common metrics used in the literature to evaluate the quality of such embeddings via clustering, both of which involve the ground truth. Our proposed method is useful because the trained model can be used to extract quality embedding on unseen tabular data. This method is one of the first to demonstrate reproducible cluster embedding on tabular data. 

6. Concerning the presentation: We have fixed the typos in equation 3 and section 3.3. We have thoroughly reviewed and revised the manuscript in the new version to improve the overall presentation.  

7. Concerning the description of the proposed method: We have updated Equation 9 with the complete loss function and a description of the proposed objective function above the equation.  

8. Concerning six contributions: We now have revised Section 2.1 (Contributions) to highlight the three most important contributions.  

9. Concerning tabular data having “low dimensions”: We now provide preliminaries on Tabular data in Section 3.1 to discuss the scope of this paper. Genomic data are very high-dimensional sequential data that can be structured in tables. Our paper does not study sequential or temporal patterns in data and focuses on standard tabular data with heterogeneous variables in many domains.

From: ICLR.cc/2023/Conference/Paper2950/Authors
title: Response to Reviewer 
comment: We appreciate your valuable feedback and the opportunity to update sections (3.1, 7.1, appendix B) and Tables (2, 3, and 5) to clarify the concerns below. 

1.	We now have included a self-contained description of tabular data in Section 3.1 (Preliminaries). 

2.	The target distribution (pij) is shown in Equation 7, following Equations 5 and 6.  The target is not derived from the embedding distribution, considering the uniqueness of tabular data. Instead, as mentioned above Equation 7, “We set pij, obtained via superior traditional machine learning, as the target to improve the autoencoder embedding (Z)”. This is because traditional machine learning of tabular data is still superior to deep representation learning in recent studies (Kadra et al. 2021, Borisov et al. 2021, Kohler et al. 2019, Smith et al. 2020, Shwartz-Ziv & Armon, 2022). 

3.	We have updated Section 5.1 (Baseline methods) and included results from several additional existing methods (DKM, CNN-GMM, CNN-K-means) in Tables 2, 3, and 5 to compare with 1-layer and 3-layer convolutional autoencoders. Because of feature vectors in tabular data, 1D convolution is considered instead of 2D image convolutional architecture. Table 3 shows that a single-layer CNN ranks 4th, being outperformed by GMM clustering of tabular data (3rd). Although the 3-layer CNN autoencoder shows superior performance on one of the seven data sets (Table 5 in Appendix C), its clustering scores are objectionably low for other data sets. Standard tabular data sets without spatial regularity (images) or temporal regularity (time series) cannot leverage the benefits of convolutional operations.

4.	In Appendix B, we detail five existing methods/architectures (DeepCluster, DKM, DCN, DEPICT, DynAE) for 2D image cluster embedding to explain why tabular data cluster embedding is not directly reproducible without customization. However, we directly used the DKM method to reproduce results on tabular data sets in Table 2, which is far worse than other baseline methods. The methodological contributions proposed for learning tabular data include 1) the selection of an independent target distribution instead of deriving from embedding distribution, 2) the choice of multivariate Gaussian distribution for multivariate tabular data over widely used t-distributed embedding, 3) fully-connected autoencoder over its convolutional counterparts, and 4) a single hidden layer with relatively smaller latent space instead of three or deeper hidden layers with 500 to 2000 neurons for image learning to avoid overfitting. These data-centric selections are justified by comparing results in Tables 2, 3, and 5, and discussed in Sections 2.1 (contributions) and 7.1 (image versus tabular data embedding).

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_89gj
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: The paper propose an unsupervised method of cluster embedding designed specially for tabular data sets. Given the motivation that existing cluster embedding methods (DEC, IDEC) proposed for image data sets may not be optimal for heterogeneous tabular data sets, the G-CEALS method is introduced by ignoring the dependence between the target distribution and embedding distribution.  Experiments on different real-world tabular datasets are conducted to validate the assumption and superiority of the proposed method.
strength_and_weaknesses: Strength:
1. This paper has clear presentation in describing the methodology.
2. The proposed method is simple but novel, which also has better performance than existing methods.

Weaknesses:
1. This paper lacks some important preliminary to make it self-contained. For example, a brief introduction about tabular data is missing. In addition, there is no formal notation denoting to the tabular data. It is unclear what the data type of tabular data, a vector or a matrix? Since dealing tabular data is the major contribution of this paper, I suggest a clarification on this aspect.
2. The inference process of some equations needs to be provided. For example, it is unclear how the target distribution is derived from the embedding distribution in Equation 4.
3. Some state-of-art methods needs to be used as comparison models for experiment. The authors claims that CNN-based methods are not compared since they only used for images. However, CNN can not only deal with image data, it can also have better performance on time-series data and data in other shapes. I suggest to also use these models for comparison experiments on tabular datasets. 
4. It is unclear why existing cluster-embedding methods for images can not be used for tabular. A very detailed explanation can better help to clarify the motivation. In addition, it is nor clear which part of the methods is specially designed for tabular data.
clarity,_quality,_novelty_and_reproducibility: This paper is written in good quality, except missing some minor statements on tabular data. The proposed method is somehow novel by introducing a new distribution for both the target and embeddings data. The model is easy to capture and reproduce. The authors have provided hyper-parameters to reproduce the results.
summary_of_the_review: This paper is in good quality both from technical or presentation aspects. However, there are some issues about statements to be addressed (see weakness parts). In addition, one major concern is about the motivation, namely why existing cluster-based methods for images can not be used for tabular data, and how the proposed method address this limitation (see the 3rd and 4th issue in weakness above). This should be clearly described and will also largely influence my final score for this paper.  
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_3YZr
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: The paper proposes a method for cluster embedding called G-CEALS. This is a modification of the typical cluster embedding method by replacing t-distributions with Gaussian clusters. The authors explain that the input and target distributions in their method become independent unlike in the competitive techniques. The architecture is composed of a single-layer AE. The performance of the model is verified on 7 tabular datasets and compared with two deep learning models, DEC and IDEC, as well as typical k-means nad GMM.
strength_and_weaknesses: The authors show that their modification leads to an improvement in the clustering performance in terms of ACC and NMI. However, the proposed method is compared with simple deep learning baselines: DEC (2016) and IDEC (2017) and classical methods: k-means and GMM. The improvement is in many cases slight. The authors excluded a few methods from the comparison because they were previously tested on images and used convolutional architecture. Since the authors reproduced the results for DEC and IDEC and changed their architecture by using only a single layer AE and the latent space of dimension 5, then they also could change the architecture of excluded methods as well. I believe that the excluded methods can also be applied to tabular data. Moreover, I do not feel that applying a single layer AE and 5 latent variables is appropriate for DEC and IDEC. If the authors want to outperform these methods, they should upgrade the proposed technique, not downgrade the competitive methods. The presented benchmark is not convincing.

I am not sure if improving the clustering ACC or NMI is the main goal of the clustering. The authors restrict their consideration to comparing the similarity of the constructed partition with the ground truth. I would like to see other arguments why the proposed method is useful.
clarity,_quality,_novelty_and_reproducibility: The paper is not well presented. There are a few typos, e.g. the norm symbol in eq 3, section 3.2 starts with a lowercase letter, etc. This makes me feel that the authors did not spend enough time on the paper.

Second, I cannot fully understand the proposed method from the description provided in section 4. What is L_cluster loss? The authors ask the reader to go back to section 3 for details. I would like to have the description of the proposed method in one place.

In section 2.1 the authors list their contributions. I feel a bit confused that the authors listed as many as six contributions. Maybe the authors should list only the most important ones, e.g. 3 points.

The authors assume that tabular data has low dimensions (page 4). I am not sure if it is a true assumption when we consider biological genomic data. Of course, I get what the authors mean, but such statements should be corrected in the paper.


summary_of_the_review: The paper could be of interest to the community, but the presentation of the paper as well as the experimental study should be improved.


correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper2950/Reviewer_wyoM
confidence: 5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.
summary_of_the_paper: The paper proposes G-CEALS, an embedding clustering method based on autoencoders. Initially, G-ceals performs clustering in the input space to define a target distribution P.  At each iteration, it performs clustering in the latent space to define the embedding distribution Q. 
A clustering loss is defined based on the KL between P and Q that is added to the reconstruction loss in order to guide autoencoder training. In this way a more 'clustering friendly' latent space is expected to emerge. 
strength_and_weaknesses: Strength
-The paper emphasizes several challenges on representation learning for clustering, specifically how to obtain better clustering representations.
-The target distribution is defined on the input space, thus the target and embedding distributions are independent.

Weaknesses
- It is questionnable whether setting the target distribution through clustering in the input space could lead to 
improved clustering performance (see comment below).
- The method is sensitive on hyperparameters (e.g. the regularization parameter \gamma in the loss function). It is mentioned that they are set into by taking account the ground truth labels. This is unacceptable in the case of clustering which is an unsupervised problem.
- There is no significant performance improvement compared to GMM and k-means (results from Table 2).    


clarity,_quality,_novelty_and_reproducibility: -The paper is generally well written and easy to comprehend.
-Implementation details are provided, however the source code is not available.
-Although the idea is somewhat novel, there are serious concerns about its effectiveness.

summary_of_the_review: The paper proposes G-CEALS, an embedding clustering method based on autoencoders. Initially, G-ceals  computes a target distribution P by clustering in the input space. Then at each iteration, it performs clustering in the latent space to define the embedding distribution Q. 
and defines a clustering loss based on the KL between P and Q. The clustering loss is added to the reconstruction loss in order to adjust the autoencoder weights. 

There are several concerns regarding the paper:
1) Setting the target distribution P through clustering in the input space essentially eliminates the advantage of using autoencoders. 
Latent space clustering is used to overcome the limitations of clustering in the input space. The proposed idea actually achieves the opposite. This is validated by the performance results in Table 2, where minor or no improvement is observed in many cases compared to k-means or GMM.
2) In Algorithm 1, computation of p_ij does not depend on the autoencoder weights, thus it should be moved in the beginning out of the for-loop.
3) In Algorithm 1, what is X_i in function 'Clustering(X_i)'?
4) Does Algorithm 1 converge? How one can set the number of epochs? 
5) The method is sensitive on hyperparameters (e.g. the regularization parameter \gamma in the loss function). It is mentioned that it is set by taking account the ground truth labels. This is unacceptable in the case of clustering which is an unsupervised problem.
6) There exist deep clustering methods that have already been tested on tabular data, such as ClusterGAN for example.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 5: marginally below the acceptance threshold