Venue: ICLR 2018 conference

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: This paper addresses the problem of embedding sets into a finite dimensional vector space where the sets have the structure that they are hyper-edges of a hyper graph. It presents a collection of methods for solving this problem and most of these methods are only adaptation of existing techniques to the hypergraph setting. The only novelty I find is in applying node2vec (an existing technique) on the dual of the hypergraph to get an embedding for hyperedges. 

For several methods proposed, they have to rely on unexplained heuristics (or graph approximations) for the adaptation to work.  For example, why taking average line 9 Algorithm 1 solves problem (5) with an additional constraint that \mathbf{U}s are same? Problem 5 is also not clearly defined: why is there superscript $k$ on the optimization variable when the objective is sum over all degrees $k$?

It is not clear why it makes sense to adapt sen2vec (where sequence matters) for the problem of embedding hyperedges (which is just a set). To get a sequence independent embedding, they again have to rely on heuristics.

Overall, the paper only tries to use all the techniques developed for learning on hypergraphs (e.g., tensor decomposition for k-uniform hypergraphs, approximating a hypergraph with a clique graph etc.) to develop the embedding methods for hyperedges. It also does not show/discuss which method is more suitable to a given setting. In the experiments, they show very similar results for all methods. Comparison of proposed methods against a baseline is missing. 



review_title: The methods presented in the paper are direct adaptation of existing techniques and rely on heursitcs to work. These methods need to be more thoroughly evaluated (among themselves, to know which method suits for a given problem) as well as against against a simple baseline. 

final_score: rating: 5: Marginally below acceptance threshold
review_content: The paper studies different methods for defining hypergraph embeddings, i.e. defining vectorial representations of the set of hyperedges of a given hypergraph. It should be noted that the framework does not allow to compute a vectorial representation of a set of nodes not already given as an hyperedge. A set of methods is presented : the first one is based on an auto-encoder technique ; the second one is based on tensor decomposition ; the third one derives from sentence embedding methods. The fourth one extends over node embedding techniques and the last one use spectral methods. The two first methods use plainly the set structure of hyperedges. Experimental results are provided on semi-supervised regression tasks. They show very similar performance for all methods and variants. Also run-times are compared and the results are expected. In conclusion, the paper gives an overview of methods for computing hypernode embeddings. This is interesting in its own. Nevertheless, as the target problem on hypergraphs is left unspecified, it is difficult to infer conclusions from the study. Therefore, I am not convinced that the paper should be published in ICLR'18.

* typos
* Recent surveys on graph embeddings have been published in 2017 and should be cited as "A comprehensive survey of graph embedding ..." by Cai et al
* Preliminaries. The occurrence number R(g_i) are not modeled in the hypergraphs. A graph N_a is defined but not used in the paper.
* Section 3.1. the procedure for sampling hyperedges in the lattice shoud be given. At least, you should explain how it is made efficient when the number of nodes is large.
* Section 3.2. The method seems to be restricted to cases where the cardinality of hyperedges can take a small number of values. This is discussed in Section 3.6 but the discussion is not convincing enough.
* Section 3.3 The term Sen2vec is not common knowledge
* Section 3.3 The length of the sentences depends on the number of permutations of $k$ elements. How can you deal with large k ?
* Section 3.4 and Section 3.5. The methods proposed in these two sections should be related with previous works on hypergraph kernels. I.e. there should be mentions on the clique expansion and star expansion of hypergraphs. This leads to the question why graph embeddings methods on these expansions have not be considered in the paper.
* Section 4.1. Only hyperedeges of cardinality in [2,6] are considered. This seems a rather strong limitation and this hypothesis does not seem pertinent in many applications. 
* Section 4. For online multi-player games, hypernode embeddings only allow to evaluate existing teams, i.e. already existing as hyperedges in the input hypergraph. One of the most important problem for multi-player games is team making where team evaluation should be made for all possible teams.
* Section 5. Seems redundant with the Introduction.
review_title: Computing node embeddings and hypernode embeddings for hypergraphs

final_score: rating: 5: Marginally below acceptance threshold
review_content: This paper studies the problem of representation learning in hyperedges.  The author claims their novelty for using several different models to build hyperedge representations.  To generate representations for hyperedge, this paper proposes to use several different models such as Denoising AutoEncoder, tensor decomposition, word2vec or spectral embeddings. Experimental results show the effectiveness of these models in several different datasets. 

The author uses several different models (both recent studies like Node2Vec / sen2vec, and older results like spectral or tensor decomposition). The idea of studying embedding of a hypergraph is interesting and novel, and the results show that several different kinds of methods can all provide meaningful results for realistic applications. 

Despite the novel idea about hyperedge embedding generation, the paper is not easy to follow. 
The introduction of ``hypergraph`` takes too much spapce in preliminary, while the problem for generating embeddings of hyperedge is the key of paper. 

Further, the experiments only present several models this paper described. 
Some recent papers about hypergraph and graph structure (even though cannot generate embeddings directly) are still worth mention and compare in the experimental section. It will be persuasive to mention related methods in similar tasks. 

it would better better if the author can add some related work about hyperedge graph studies. 
review_title: interesting, but the presentation needs to be improved

Meta-review: While there are some interesting and novel aspects in this paper, none of the reviewers recommends acceptance.
Decision: Reject