HyperQuery: A Framework for Higher Order Link Prediction
Authors: Sepideh Maleki
Josh Vekhter
Keshav Pingali
Venue: Submitted to ICLR 2023 (2023)
Keywords: link prediction
Hyperedge prediction
Hypergraph learning
message passing
hypergraphs

Abstract: Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life.  While graphs are a natural way to represent complex networks and are well studied, typical approaches to modeling group membership using graphs are lossy.  Hypergraphs are a more natural way to represent such ``higher order'' relationships, but efforts to apply machine learning techniques to hypergraph structured datasets have been limited thus far.  In this paper, we address the problem of link prediction in knowledge hypergraphs as well as regular hypergraphs and develop a novel, simple, and effective optimization architecture to solve this task. Additionally, we study how integrating data from node-level labels can improve the results of our system. Our self-supervised approach achieves significant improvement over state of the art results on several hyperedge prediction and knowledge hypergraph completeion benchmarks. 

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HYPERQUERY. A FRAMEWORK FOR HIGHER ORDER LINK PREDICTION
Anonymous authors Paper under double-blind review
ABSTRACT
Groups with complex set intersection relations are natural way model a wide array of data, from the formation of social groups to the complex protein interac- tions which form the basis of biological life. While graphs represent complex networks and are well studied, typical approaches to modeling group membership using graphs are lossy, Moreover, a simple graph based ap- proach cannot be used for prediction and classification over a collection of entities. Hypergraphs are more natural way to represent such "higher order" relationships, but efforts to apply machine learning techniques to hypergraph structured datasets have been limited thus far. In this paper, we address the problem of link prediction in knowledge hypergraphs simple, and effective optimization architecture to solve this task. Additionally, we study how integrating data from node-level labels can improve the results of our system. Our self-supervised approach achieves significant improvement over state of the art results on several hyperedge prediction and knowledge hypergraph completion benchmarks.
natural way
well as simple hypergraphs and develop novel,
INTRODUCTION
There is significant demand for applying learning to graph structured data over the past couple of years. While graphs can accurately model binary relations between entities, they are not natural representation n-ary relations between entities. For example, a protein complex network cannot be represented by graph since a protein complex might be created only in presence of more than two proteins Giurgiu et al. (2019). In this paper, we set out to answer complex queries that go beyond a simple graph i.e. the current graph learning algorithms cannot solve such problems without major modifications. In particular, we study Learning on Hypergraphs.
Hypergraphs are generalization of graphs for representing such n-ary relations. Formally, hypergraph H is tuple (V, E)) where V is set of nodes; E 2| is set of nonempty subsets of V called hyperedges. Similarly, a knowledge hypergraph is a generalization of a knowledge graph where relations are between any number of entities. Recent research shows that hypergraph models produce more accurate results even in problems in which graphs are used to represent n-ary relations Zhou et al. (2006); Feng et al. 22020) Fatemi et al. (2019).
In this paper, we aim to solve the task of hyperedge prediction on both simple and knowledge hypergraphs. Hyperedge prediction in simple hypergraphs is analogous link prediction in graphs, and can be formally defined as follows: given hypergraph H (V. E)) and k-tuple of nodes (V1, U2 .... Ux). predict whether this tuple a hyperedge or not. While link prediction in graphs is well-studied problem, hyperedge prediction has not received adequate attention in spite of its many applications. For example, can be used to predict new protein complexes, drug-drug interactions, new collaborations in citation networks, discover new chemical reactions in metabolic networks, etc Yadati et al. (2020); Giurgiu et al. (2019); Piñero et al. (201)). Hyperedge prediction a more challenging problem than link prediction in graphs. Formulating this problem link prediction problem in graphs is a lossy operation, reducing the accuracy of predictions Kirkland (0017):
et al. 2018).
In knowledge hypergraphs, it is often necessary to not only predict new hyperedges but also their type. For example, in protein-drug genomics knowledge hypergraph, it is important to predict

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HEdge
Bird HEdge A
Cot HEdge
Prediect Type
High order hyperadge embeedelng
HEdge
???
HEdge
Dog
Negative Type Lobel
Figure/ I: The HyperQuery Inference Problem: In this paper, prefer to work with the star-expansion representation of hypergraph (left). We are interested in studying hypergraphs and knowledge hypergraphs with categorical labels (types) stored the edges (center). Our primary objective to create a system that predicts the existence of hyperedge and its type.
not only drug-drug interactions but also the type of these interactions that describes the side effects Zitnik et al. (2018). This generalized hyperedge prediction problem can be described formally as follows: given knowledge hypergraph K (E, R) and a tuple of entities (el, Eg,... ex), we want to predict if this tuple forms hyperedge and if so, what its rype is. This problem setting is illustrated figure
This paper makes the following contributions.
We describe HyperQuery, a neural message passing based framework that is designed find embeddings of hyperedges in semi-supervised fashion.
HyperQuery:
Novel feature extraction: We use clustering to extract global features of nodes and hyper- edges.
Higher order link prediction: We solve hyperedge prediction on simple hypergraphs as well as knowledge hypergraphs.
The pipeline of our system is shown in figure
RELATED WORK
Link prediction in graphs: There are two ways to address the link prediction problem in networks. One approach is to learn an embedding of the nodes of graph and then apply function on these embeddings to obtain the embedding of an edge. We call this approach an indirect approach solve hyperedge prediction. For example, node2vec Grover & Leskoved (0016), and deepwalk Perozzi et al. (2014) are random-walk based approaches and Vashishth et al. (2019); Davidson et al. (2018) GNN-based approaches for graphs that learn the embedding of the nodes and then operator such as average to compute the embedding an edge i.c. given two nodes u, and v, they apply binary operator
binary
generate embedding of g(u, v) such that g V V Rd where is the dimension of the embedding. Direct approaches in graphs learn the embedding of edges directly and apply that the link prediction problem. Examples of this approach includes path-based approaches such as Zhu et al. (2021); Sadeghian et al. (2019). One popular task in knowledge graphs predict missing relations between entities. This task is called knowledge graph completion and one could think of it as a generalization of link prediction in graphs. The problem of knowledge graph completion has been studied extensively for example: Zhhu al. (202T): Wang et al. (2020);
Rossi et al. 2022)
Hyperedge prediction: Link prediction in hypergraphs can also done indirectly by first com- puting the embedding of the nodes of the hypergraph and then applying function to the tuple vx) ) to obtain the embedding of the tuple i.e. hyperedge. The difficulty with such models
(V1, U2, U2,,U2,-.. is that for hypergraphs, function g must be nonlinear to capture higher-order proximity of nodes in the hypergraph| Tu et al. (2018). This means it is not good design choice to use an operator such as average obtain the embedding of hyperedge from its nodes. Related works HyPerSAGNN and NHP have used non-lin con-linear functions such graph neural networks Zhang et al.) (2020); Yadati et al. 2020 compute the embedding of hyperedge from its nodes. Directly learning the embedding of
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hyperedge and applying hyperedge prediction to that embedding has not been studied. To the best of our knowledge, we are the first to approach the problem in this manner.
Link prediction in knowledge hypergraphs is relatively under explored. Most approaches generalizes knowledge graph based methods to work with n-ary relations. More recent work on this area propose novel methods that directly works with knowledge hypergraphs such as Fatemi et al. (2019) Wang et al. 2021).
Random Walk Based Feature Generation for hypergraphs: In problems in which nodes do not have features, the first step is to generate features for the nodes. The most common approach is to use node2vec. For example, HyperSAGNt Zhang al. (2020) first generates features using node2vec and then passes these features through an attention layer. During inference, the embedding of a proposed tuple of nodes computed using a one layer, position feed-forward network. They can also use the corresponding row of the adjacency matrix to extract features. Similarly, NHP runs node2vec on the clique expansion of a hypergraph and then uses a GCN layer to improve these features. Finally, they pass these embeddings to scoring layer Yadati et al. (2020).
Clustering Based Feature Generation: Random-walk based approaches are one way to generate features for hypergraph, but they only exploit the local connectivity of nodes in the hypergraph. In this paper, we investigate the effectiveness hypergraph clustering algorithms for feature extraction.
Clustering has been used to understand the structure of complex networks. A cluster in hypergraph partition of nodes into sets that are similar to each other and dissimilar from the rest of the hypergraph. Intuitively, a cluster is group where nodes are densely inter-connected and sparsely connected to other parts of the network. Placing the embedding of such nodes closely in the embedding space can be useful in many graph mining tasks such as clustering, node classification, network reconstruction and link prediction [Bhowmick et al. (2020). A classic clustering algorithm in hypergraphs is the FM (Fiuuceia & Mattheyses) (1982) algorithm: given initial assignment of nodes to clusters, this algorithm moves node to the cluster that results in the largest reduction in connectivity between clusters. Multi-level clustering approaches such Karypis et (199);;
Devine et al. (206)); Maleki et al. (202T) build on this algorithm and improve the performance of FM algorithm by successively coarsening the hypergraph, finding clusters in the smallest hypergraph, and then interpolating these to the coarser hypergraphs, applying the FM algorithm at each level. In this paper, we use a recent work called BiPart, Maleki et al. (202T), for clustering to generate initial features of the hyperedges well as nodes of a hypergraph.
3 HYPEREDGE CONVOLUTION OPERATOR
We begin with the question of how one might build a system to "answer" HyperQueries. Given a collection of nodes, our HyperQuery oracle will answer questions such as whether these nodes related. Ultimately, our goal is to perform prediction and classification on a collection of nodes.
In this section, we start by studying the question of inference in knowledge hypergraphs, where a vector of data is stored on entities and relations. We present an approach for defining trainable convolutions on hyperedges which is well suited for performing inference for knowledge hypergraph completion. In the next section, we will discuss the pre-processing approach that completes our framework for performing hyperedge prediction on simple hypergraphs.
A basic approach for defining a HyperEdge convolution operator proceeds in two steps. First, we set out to aggregate and summarize the known label data the neighborhood of the hyperedge e or query set of node in question. Then, we apply learned weight matrix W and pass it through the non linearity function a.
hh oWW 26hh You e N((e))
(I)
To fully unlock the power of modern machine learning, we set out to create a trainable system. In fact, improve on Equation [ and propose something more general. A flexible, composable, trainable,
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W
???
AGG
2kh, Vig g)
AGG
Ω
Figure 2: HyperEdge Convolution Operator. A HyperQuery can be passed by specifying a set of nodes q into the system (left). For each node, first aggregate over its neighboring hyperedges update its embedding, then for each hyperedge we perform summary function Ω2 to compute what we call the harmonic statistic HQ. (right) By adding fully connected layer W and a nonlinearity o in series with this calculation, we arrive at our proposed HyperEdge convolution operator.
hyperedge message-passing based (i.e. scalable) operation for learning to answer HyperQueries:
h AGG(N Ye N(e)) hs (( E W(e)))
(2)
(3)
h = o(W* hs
(4)
For each node v in hyperedge e, we aggregate along it's hyperedge neighbor features to calculate h Then, for each hyperedge e, we aggregate the messages from its nodes (i.e., h, E (W(e)), using summarization function (2..) as shown above. Finally, we have a hidden "deconvolution" layer and a non-linearity. The he; above amounts a "mean-fiell embedding of each node e the average of a sampling of the data stored on the hyperedges is connected to.
This concludes the first part of approach to learning useful representations of HyperQueries. Intuitively, this message passing based aggregation and summarization process can be thought of diffiusion process flow, which averages and symmetrizes the edge level data by effectively performing step of Laplacian smoothing.
In knowledge hypergraph, we can effectively learn the hidden weights W by choosing the initial feature b. of a hyperedge he to be the one hot vector of its type, and building up an autoencoder style problem. By repeating this iteration twice, we already arrive an effective tool for knowledge hypergraph completion which generalizes to unseen data far better than benchmark approaches. In Table 6 we outline our performance relative to other benchmarks. We achieve this performance with straightforward model, we simply treat the output h2 as predicted class label P(e). From there we minimize the loss below as a function of hidden layer weights W and W
L= L= Σ J(P(e),
(5)
In our objective function, we take (-) to be the cross entropy loss, e to be a hyperedge in the training dataset D, Pe) is the predicted type of hyperedge e, and G(e) is the actual ground truth type (relation) of hyperedge in the dataset.
ANSWERING HYPERQUERIES ON SIMPLE HYPERGRAPHS
Our main focus in this paper is the task of hyperedge prediction, i.c. given an simple hypergraph and set of nodes (1i,.., v,), predict whether this tuple forms a hyperedge.
In this setting, there is no additional label data such as knowledge hypergraphs and thus inference must be computed entirely from the hypergraph strueture. Thus if we want to make use of a flow based approach, need a way of computing useful initialization. Our insight is that useful initial categorical embeddings can found by existing clustering algorithms, which works by recursively finding balanced cuts of hypergraph.
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Community
Max Pooling for Edge Labels
Detecton
Node
C(A) 2
Figure 3: Generating Useful Labels using clustering: Not all hypergraph data comes with labels (left) but so far approach has depended on having categorical labels on the edges and nodes. We leverage hypergraph clustering to first assign cluster id as labels to the nodes, obtaining an initial cluster assignment e (center), which then propagate the hyperedges via Max Pooling (right)
in order to obtain the edge cluster assignment co. We use to as the data in L(h).
4.1 FEATURE EXTRACTION USING CLUSTERING
One way learn an embedding that captures meaningful structural information about a hypergraph is to run random- mandom-walk based algorithms such as node2vec Grover & Leskovec (2016). Previous works on hyperedge prediction such as HyperSAGNN Zhann al. (2020) and NHP Yadati et al. (2020) use node2vec to first learn feature vectors for nodes of hypergraph represented in variety of ways. Then, they improve these features using attention-based methods. However, such methods have number of drawbacks:
They do not learn the correlation between nodes that do not appear the same random walk, might require many samples to capture effects of weak correlations.
2. Random walks explore only the local properties of the hypergraph, optimization might get stuck in local minima.
3. Random walks on hypergraphs mix very quickly and thus even if an algorithm converges to good answer, will likely require many samples/computation converge.
4. The published methods learn node based features and they do not learn feature vector of hyperedges directly, couldn't be directly applied to our architecture.
It occurred to that instead, it is possible to use state-of-the-ar partitioning based clustering tools as an alternative approach for pre-computing features. While clustering is well studied problem in ML, for instance has been used in prediction as early in 2015 Deylami & Asadpour (2015), is not used by any of the oftee----hh-rrr prediction tools today, and therefore, merits revisiting, given the simplicity and effectiveness of the approach evaluate in this paper.
In particular, for our HyperQuery flow, we want an initial label assignment that is "smooth" in a way that is well defined for the given hypergraph topology. To do this, we clustering algorithm that partitions the nodes of the hypergraph into clusters. Each cluster of nodes is given a unique integer id. To transfer these labels onto hyperedges, we perform a max-pooling step (described in more detail in Figure 3
Cut-Metric for Hypergraphs. For our purpose, we use any clustering algorithm. In experiments, we use multilevel clustering algorithm that partitions nodes into given number of clusters while minimizing the hyperedge cut, defined below. While there is not unique canonical way to defin hyper-edge cut, this approach worked well and exposes the number of clusters as hyper-parameter the system.
cut - [
(6)
Here, H is the hypergraph, C' is the partition of nodes into clusters, and Xe C) is the number of clusters that hyperedge e spans. Intuitively, nodes that belong to the same cluster are considered similar. This is similar to approaches like node2vec in which nodes that appear in the same random walk are considered to be similar.
OPTIMIZING THE HYPEREDGE CONVOLUTION OPERATOR
Here outline few important technical details that significantly improve framework.
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(
Chemboon Meriion
Figure 4: Learning W Given hypergraph with labels on nodes and edges, we experiment with zoo of choices for Q. In this illustration, we convolve once, multiply by W and a and then pass through fully connected layer to return to space of the same dimension of hyperedge types. Finally we then train as an autoencoder.
5.1 NODE CLUSTER AS FEATURE
The initial aggregation step AGG in convolution operator comes from the idea that reasonable first way to think about creating embeddings for hyperedges is to simply average node embeddings. However, this simple measure fails to capture important information regarding the distribution of node embeddings within hyperedge.
To fix this problem, augment every node feature vector with the one-hot encoding of the node cluster id, as seen in Equation 7
h CONCAT(AGGII E (N()),
where AGG(.) is an aggregation function, and x, is the one-hot partition id of node. If nodes of a hypergraph have features themselves, these features can also be concatenated with 2..
5.2 CHOOSING THE RIGHTS Ω
In this work, evaluate three different types of summary statistics for Ω (Figure 4 center). A component-wise mean and variance, and a sort of "robust variance" estimator we call minmax (element-wise difference of maximum and the minimum values of the vectors) similar the one used in NHP Yadati et al.) (220)) to achieve state of the art performance. Intuitively, when Ω is the mean, convolution maps hyperedges to the average embedding of constituent nodes, whereas the variance measures how correlated different nodes are with each other. In our experiments in Section 6, we find that for the hyperedge prediction, minmac/variance performed better as choice of Ω whereas in knowledge hypergraph completion, mean worked better.
We also augment these aggregations better capture the correlation between different labels/com- munities by introducing bilinear aggregation layer Zhu & Koniusz (2021). Bilinear aggregation has significantly improved visual concepts recognition Koniusz et al. (2017). and practice also generally improves the accuracy of our results. Specifically, we create an auto-correlation mulrix by multiplying a hyperedge feature vector by itself. This matrix has dimension d x d, which we flatten.
5.3
AUGMENTED CONVOLUTION OPERATOR
Our final scheme for hyperedge message passing is the following:
Ω 24 Ve E (e)))
(8)
h (WW flat(n)
Where hy is computed using Equation Q is an aggregation function, flat(.) flattens the correlation matrix and stores it in column vector, AGG(.) takes the element-wise mean of the hyperedge

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feature vector, Te is the feature vector of node e, and W is the trainable weight matrix. The effect of using different aggregation functions is explored empirically in Table
Time complexity. We analyze the time complexity of framework (Equations 7 and in terms of the size of the hypergraph, assuming the number of relations (types) is independent of the size of the hypergraph. Let denote the number of hyperedges and denote the number of nodes. Let (eg(v;) denote the degree of node U, and let Å denote maz1gisndeg("!) For Equation our framework takes (n Á) time. For Equation let deg(e;) denote the degree of hyperedge e; and let A denote mazigigm deg(e))))) Equation 8 takes O(m A) time. Finally, the time complexity of Equation is constant since the number of labels is independent of the size of the graph. Overall, our framework takes O(m A) O(n A).
5.4 MODEL EXPLAINABILITY
The ideal initial feature vector for hyperedge should include local and global properties of the hypergraph. In our model, clustering exposes global properties. Specifically, we keep track of the cluster id of hyperedges as well as the distribution of labels on the nodes in the neighborhood of hyperedge. Intuitively, Hyperedges that are in the same cluster have similar label distribution their nodes are similar to each other and by assumption, they are related. Previous work [rroerr & Leskoved 6): Perozzi al. (2014) has shown that placing such similar nodes closely in the embedding space will facilitate tasks such as node classification and link prediction. We follow the same intuition.
The message-passingg scheme of labels is conceptually similar to label propagation Raghavan et al. (0007). The objective of the label propagation algorithm is assign each node into cluster with the most number of its neighbouring nodes. Intuitively, this scheme also put hyperedges with the same label/cluster closer the embedding space facilitating hyperedge prediction for both knowledge hypergraphs and simple hypergraphs.
EXPERIMENTS
We evaluate our framework HyperQuery on knowledge hypergraph completion task well as hyperedge prediction and show that our architecture outperforms the state the arts for these tasks. Furthermore, we conduct ablation study understand the effectiveness of the major HyperQuery kernels. The details of our setting are in Appendix A.
6.1 KNOWLEDGE HYPERGRAPH COMPLETION
We first evaluate our system for the task of link prediction for knowledge hyperedges i.e. knowledge hypergraph completion. We evaluate our system on three datasets: FB-AUTO, M-FB15K, and JF17K. We used the same test, train, and validation sets as Fatemi et al. (019). We use MRR (mean reciprocal rank) and @it@1 1, (hit ratio with cut-off values
and 3) as our evaluation metrics.
The datasets used in this section are standard knowledge hypergraph datasets from previous work Fatemi et al. (2019). The summary of the knowledge hypergraphs are Table FB-AUTO, M-FB15K Fatemi et al. 2019), and JF17K Wenn et al. (2016) are knowledge hypergraphs with n-ary relations that is collected from Freebase dataset.
Datasets:
Table 1: Knowledge hypergraph dataset
DATA SET
R
#train
#valid
#test
FB-AUTO
3,410
8
6,778
2,255
2,180
M-FB15K
10,314
71
415,375
39,348
38,797
JF17K
29,177
327
77,733
15,822
24,915
We compare our results with the following baselines: HSimplE, and HypE two embedding based approaches for knowledge hypergraphs introduced by Fatemi al. (201)). Both methods find the
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AUC
USPT
(01166
Number Cammunittes
Figure Performance of HyperQuery for different numbers of clusters.
embedding of an entity based on its position in relation. M- M-DistMult Yang al. (2014) defines a scoring function for each tuple (e1, (1,,71,0 (g.r 62). We modify this so that each relation could have any number of entities. M-TransH is modified standard knowledge graph scoring function (TranshH) that accepts beyond binary relations. Finally, M-CP Hitchcock (927) is tensor decomposition approach. We apply similar approach as Fatemi et al. (2019) extend it beyond binary relations.
We used HyperQuery to perform knowledge hypergraph completion. Table summarizes the result of our experiment. HyperQuery performs the best compared to all other baselines all metrics. Specifically, on metric Hit@ against the best baseline, improves to 5% on dataset FB-AUTO, 18% M-FB15K, and more than 50% JFI7K.
Table 2: Knowledge Hyperedge Completion.
FB-AUTO
M-FB15K
JF17K
MRR
Hir@
Hir@3
MRR
Hit@1
Hir@
MRR
Hir@
Hit@3
HYPERQUERY
91.5
83.1
99.9
95.1
90.5
99.7
99.9
99.1
99.9
HSIMPLE
79.8
76.6
82.1
73.0
66.4
76.3
47.2
37.8
52.0
HYPE
80.4
77.4
82.3
77.7
72.5
80.0
49.4
40.8
53.8
M I-DIISMMLT
78.4
74.5
81.5
70.5
63.3
74.0
46.3
37.2
51.0
M-TRANSH
72.8
72.7
72.8
62.3
53.1
66.9
44.4
37.0
47.5
M-CP
75.2
70.4
78.5
68.0
60.5
71.5
39.1
29.8
44.3
6.2 HYPEREDGE PREDICTION
The second task we study in this paper is hyperedge prediction. evaluate our system on four datasets: iAF1260b, iJO 366366 USPTO, and DBLP. We used 70% of the hyperedges in these for test, 10% for validation and 20% for training. The summary of these datasets are in Table
Table 3: Hyperedge prediction dataset
DATA SET
NODES
HYPEREDGES
TYPE OF DATA
IAF1260B
1,668
2,084
METABOLIC REACTIONS
1J03666
1,805
2,253
METABOLIC REACTIONS
USPTO
16,293
11,433
DBLP
20,685
30,956
CO-AUTHORSHIP
iAF1260b' metabolic reaction dataset for specie E. coli. We use this dataset for hyperedge prediction where our goal is to predict missing reactions i.e. hypereges. In this dataset each reaction considered hyperedge connecting its participating metabolites (nodes).
iJ01366 a metabolic reaction dataset similar to iAF1260b. USPTO 2 organic reaction dataset. We used subset of chemical substances that only contains carbon, hydrogen, nitrogen, oxygen,
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phosporous, and sulphur. DBLP co-authorship publication dataset. We used subset of papers published in only Al conferences: AAAI, IJCAI, NeurIPS, ICML, CVPR, ICCV, ACL, NAACL, etc. Each author in this dataset is node and papers represent hyperedges connecting authors of paper.
We compare our results with previous works: NHP Yadati et al. (2020), HyperSAGNN Zhang et al. (2020), HyperGCN Yadati al. (2019), and node2vec Grover Leskoved 2016). The description of these methods are in 2 We use a similar negative sampling strategy as NHP Yadati et al. (2020). Motivated by NHP, we investigate another aggregation function for approach. We call this aggregation function minmax which is the element wise difference of max and min values of the embedding vectors in equation Furthermore, we also experiment on using operator variance as an aggregation function. These results is summarized in Table We use 16 communities for this experiment. In Section 6.3 we discuss the effect of different number of communities.
HyperQuery with minmax aggregation function performs the best on all datasets in this paper. Comparing with NHP, on their minmax operator, HyperQuery minmax outperform them by up to 7% on iAF1260b, 5% iJ01366, 1.5% USPTO, and 1.8% on DBLP; mean aggregation operator, HyperQuery outperforms NHP by up to 6% on iAFI260b, 4.6% on iJO1366, 12% on USPTO, and 13.6% on DBLP. HyperQuery outperforms HyperSAGNN HyperGCN by more than 4%. Finally, node2vec results show poor performance on hypergraph datasets showing that graph based approaches are not suitable for hypergraphs.
all datasets by more than 6%, and
6.3 ABLATION STUDY
We study the behaviour of each component of HyperQuery. First, we study the effect of bilinear pooling on hyperedge prediction. Table ( shows this effect. On the larger dataset, USPTO, the bilinear pooling improves the quality of our framework by 5.6% for minmax. Similarly, for DBLP, the improvement is about 2%. On the smaller datasets, bilinear pooling does not make significant change.
Next, we study the effect the number clusters in our dataset. Figure how the performance of our framework changes iJO1366, the performance improves as we increase the number of clusters up to 16 clusters and then decreases. This behaviour is expected since we increase the number of clusters, the quality of these clusters decreases (i.e., the hyperedge cut increases). However, if the number of clusters is very small, we exploring the global structure of our hypergraph enough which again decreases the performance of our framework.
increase decrease the number of clusters. For all datasets except
Table Area Under Curve (AUC) scores for hyperedge prediction. NOPOOL refers the model without bilinear pooling. HQ is our proposed model.
IAF1260B
IJ01366
USPTO
DBLP AUC
AUC
AUC
AUC
HQ-MINMAX
72.2
68.5
75.7
72.0
HQ-MEAN
66.5
65.9
72.2
69.6
HQ-VAR
71.1
68.1
75.0
71.3
HQ NOPON..
72.7
68.9
70.
70.4
HQ HO-MEAN-NOPOOL
67.6
65.7
70.6
65.7
HQQVAR-NOPOOL
72.3
67.5
74.1
71.6
NHP-MINMAX
64.3
63.2
74.2
69.2
NHA--MENN
60.5
61.2
65.5
56.4
HYPER-SAGNN
60.1
$6.3
67.1
65.2
HYPERGCN-MINMAN
64.0
62.2
70.5
67.4
NODE2VEC-
BENRZVEE-MINMAA MINMAX
66.0
62.0
71.0
67.0

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REFERENCES
Ayan Kumar Bhowmick, Koushik Meneni, Maximilien Danisch, Jean-Loup Guillaume, and Bívas Mitra. LouvainNE: Hierarchical Louvain Method for High Quality and Scalable Network Em- bedding &, In 13th ACM International WSDM Conference, WSDM '20: Proceedings of the 13th International Conference on Web Search and Data Mining, pp. 43-51 February 2020. doi: 10.114 5/3336191.3371 1800
URL htth:tt:: http://:w...ccceeeeeeeeeeeeeeeea
Tim R. Davidson, Luca Falorsi, Nicola De Cao. Thomas Kipf, and Jakub M. Tomczak. Hyperspherical variational auto-encoders. 2018. doi: 10.48550/ARXIV.180 1804.0001.. URL httts::/aaaa..
org/ org/abs/ 1804. 00891
Karen D. Devine, Erik G. Boman, Robert T. Heaphy, Rob H. Bisseling, and Umit V. Catalyurek. Parallel hypergraph partitioning for scientific computing. In Proceedings the 20th International Conference on Parallel and Distributed Processing, IPDPS'06 06, pp. 124, Washington, DC,
USA, 2006. IEEE Computer Society. ISBN 1-4244-0054-6. URL http: /dl acm. org/eit
ation w www....fffidi118895555 1899056
Hasti Akbari Deylami and Masoud Asadpour. Link prediction social networks using hierarchical community detection. In 2015 7th Conference on Information and Knowledge Technology (IKT), pp. 1-5, 2015. doi: 10. 109/1KT.2015.7288777
Bahare Fatemi, Perouz Taslakian, David Vazquez, and David Poole. Knowledge hypergraphs: Prediction beyond binary relations, 2019. URL http:/tsss//aaxiiioooot wtt.oo///g////........0 00137
Song Feng, Emily Heath, Brett Jefferson, Cliff Joslyn, Henry Kvinge, Hugh Mitchell, Brenda Praggastis, Amie J. Eisfeld, Amy C. Sims, Larissa B. Thackray, Shufang Fan, Kevin B. Walters, Peter J. Halfmann, Danielle Westhoff-Smin -Siith, Qing Tan, Vineet D. Menachery, Timothy Sheahan, Adam S. Cockrell, Jacob F. Kocher, Kelly G. Stratton, Natalic C. Heller, Lisa M. Bramer, Michael S. Diamond, Ralph S. Baric, Katrina M. Waters, Yoshihiro Kawaoka, Jason McDermott, and Emilic Purvine. Hypergraph models of biological networks to identify genes critical pathogenic viral response, 2020. URL htttp:://arxiv.rrrggg/////// abs 2010. 03068
C.M. Fiduccia and R.M. Mattheyses. A linear-time heuristic for improving network partitions. In 19th Design Automation Conference, pp. 181, 1982. doi: 10.1109/DA.119 1982.154992
M Giurgiu, Reinhard, B Brauner, I Kangger-Katenbach,, G Fobo, Frishman, C Montrone, and
A. Ruepp. CORUM: the comprehensive resource of mammalian protein complexes-2019. Nucleic Acids Research, 2019.
Aditya Grover and Jure Leskovec. node2vec: Scalable feature learning for networks, 2016.
Frank L. Hitchcock. The expression of tensor or a polyadic sum of products. Journal of
Mathematics and Physics, 181-4)1164-88, 1927, doi: http:://0hioogg//0000000//pppppp com/ comm/doi/annn URL https:://wwwnelliieb.tte http://wwwwcoooaaoaa/////....... 1002/ http:////ap11m////
George Karypis. Rajat Aggarwal, Vipin Kumar, and Shashi Shekhar. Multilevel hypergraph partition- ing: Applications in vlsi domain. IEEE Trans. Very Large Scale Integr. Syst., 7(1):69-77, March 1999. ISSN 1063-8210.
Steve Kirkland. Two-mode networks exhibiting data loss. Journal of Complex Nenworks, 6(2): 297-316 08 2017. ISSN 2051-1329. doi: 10. 10.1093/comnee/cnx00.. URL htthhttps:/ /attps://doi.ors 10.
Piotr Koniusz, Fei Yan, Philippe- Henri Gosselin, and Krystian Mikolajezyk. Higher-order occurrence pooling for bags-of-words: Visual concept detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(2):313-326, 2017. doi: 10. 1.111/9TPAM.22016
Sepideh Maleki, Udit Agarwal, Martin Burtscher, and Keshav Pingali. Bipart: A parallel and deterministic hypergraph partitioner. SIGPLAN Not., 2021. doi: 10. 1114/3337801.3441611
10

---

Under review as a conference paper at ICLR 2023
Sepideh Maleki, Donya Saless, Dennis P. Wall, and Keshav Pingali. Hypernetvec: Fast and scalable hierarchical embedding for hypergraphs. In Pedro Ribeiro, Fernando Silva, José Fernando Mendes, and Rosário Laureano (eds.), Network Science, pp. 169-183, Cham, 2022. Springer International Publishing. ISBN 978-3-030-97240-0.
Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. Deepwalk: Online learning of social repre- sentations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '4, Pp. 701-710, New York, NY, USA, 2014. ACM. ISBN 978-1-4503--256-9 doi: 10.1145526233302222332222 URL http: /ttp:://dooo acm. org /10. 114 5/2623330.2585 2623732
Janet Piñero, Juan Manuel Ramirez-Anguite Josep Saüch-Pitarch, Francesco Ronzano, Emilio Centeno, Ferran Sanz, and Laura Furlong. The DisGeNET knowledge platform for disease genomics: 2019 update. Nucleic Acids Research, 48(D1))DD855555885 11 2019. ISSN 0305-1048. gkz1001 doi: 10. 00.1093//ar/gkz1001 /tt.https::/aal..orggg.ogog..ooo
Usha Nandini Raghavan, Reka Albert, and Soundar Kumara. Near linear time algorithm to detect community structures large-scale networks. Physical Review E, 76(3), sep 2007. doi: 10.1103/
physreve.76.036106
Andrea Rossi, Donatella Firmani, Paolo Merialdo, and Tommaso Teofili. Explaining link predic- tion systems based on knowledge graph embeddings. In Proceedings of the 2022 International Conference on Management of Data, SIGMOD '22. pp. 2062-2002000000 2075, New York, NY, USA, 2022. Association for Computing Machinery. ISBN 978 9781450392495. doi: 10.1145/351 012/:554421.1117771
351 4221 7887
Ali Sadeghian, Mohammadreza Armandpour, Patrick Ding, and Daisy Zhe Wang. Drum: End-to-ent differentiable rule mining on knowledge graphs, 2019. URL https: http://xxvv.orrr. orw./bs//laaaaa.......o/
00055
Ke Tu, Peng Cui, Xiao Wang, Fei Wang, and Wenwu Zhu. Structural deep embedding for hyper- networks, 2018.
Shikhar Vashishth, Soumya Sanyal, Vikram Nitin, and Partha Talukdar. Composition-based multi- relational graph convolutional networks, 2019. URL
3082
Hongwei Wang. Hongyu Ren, and Jure Leskovee. Relational message passing for knowledge graph completion, 2020. /RLp:tttps////rx...orrrr http://aaab///...2222..
Quan Wang. Haifeng Wang. Yajuan Lyu, and Yong Zhu. Link prediction n-ary relational facts: A graph-based approach, 2021.
http://www.org/////1/0e///// 08476
Jianfeng Wen, Jianxin Li, Yongyi Mao, Shini Chen, and Richong Zhang. On the representation and embedding knowledge bases beyond binary relations, 2016. URL abs/1604.r 08642)
Naganand Yadati, Madhav Nimishakavi, Prateek Yadav, Vikram Nitin, Anand Louis, and Partha Talukdar. Hypergen: new method of training graph convolutional networks on hypergraphs, 2019.
Naganand Yadati, Vikram Nitin, Madhav Nimishakavi, Prateck Yadav, Anand Louis, and Partha Talukdar. Nhp: Neural hypergraph link prediction. In Proceedings of the 29th ACM International Conference Information and Knowledge Management, CIKM '20, New York, NY, USA, 2020. Association for Computing Machinery, ISBN 978 178149036,,99 doi: 10.1145/334053 1.31 1.311
URL /ttp::://oo...og//00111/////////
3411870
Bishan Yang, Wen-tau Yih, Xiaodong He, Jianfeng Gao, and Li Deng. Embedding entities and relations for learning and inference in knowledge bases, 2014. URL htt.hhttss///ai......m org/
abs/ 0tt//112..677
Ruochi Zhang, Yuesong Zou, and Jian Ma. Hyper a self-attention based graph neural network for hypergraphs. In International Conference on Learning Representations (ICLR), 2020.
11

---

Under review as a conference paper at ICLR 2023
Dengyong Zhou, Jiayuan Huang, and Bernhard Schölkopf. Learning with hypergraphs: Clustering, classification, and embedding. In B. Schölkopf. J. Platt, and T. Hoffman (eds.), Advances in Neural Information Processing Systems, volume 19. MIT Press, 2006. URL 6d (e
neur (ee0://s...c/ppprrr////////1ee/0 er.pdf
Hao Zhu and Piotr Koniusz. Graph convolutional network with generalized factorized bilinear aggregation, 2021. URL
Zhaocheng Zhu, Zuobai Zhang, Louis-Paseal Xhonneux, and Jian Tang. Neural bellman-ford networks: A general graph neural network framework for link prediction, 2021. URL https //arxiv.org/aattet..e
06935
Marinka Zitnik, Monica Agrawal, and Jure Leskovec. Modeling polypharmacy side effects with graph convolutional networks. Bioinformatics, 34(13):457-466 2018.
A DETAILS ON HYPERQUERY SETTINGS
Negative Sampling, We use similar approach to Yadati et al. (2020) i.c for each hyperedge in our dataset, create hyperedge e' by having half of the vertices sampled from the remaining half from V - e. This sampling method is motivated by the chemical reaction datasets where it is unlikely that half of the substances of valid reaction (from e) and randomly sampled substances (from V - e) are involved in another valid reaction.
The number of clusters used in the evaluation section of this paper 16. Furthermore, we showed the effect of using different number of clusters in Figure We use 2 layers of hyperedge convolution our test implementation.
Hypeerparaameers.
Operator Ω. for given set of vectors I1,..., I' E Rd
MINMAX(F1 .... mb, = (max VAR( [1 ...... [b)) (variance((aa)) kk] 1, ..., d
min FaI), s k]. | 1, d
(10)
(11)
MEAN (II....., Fk) = (MEAN(())) kk] [ I,.... d
(12)
B CLUSTERING ALGORITHM
In this paper we use BiPart Maleki et al. 2021 as our clustering algorithm. BiPart is a multilevel and deterministic hypergraph partitioner. Given number k. BiPart partitions the nodes the hypergraph into k disjoint blocks. In our framework, we use BiPart as pre-processing step where we partition the nodes of a hypergraph first and the we use the one hot vector of their partition id as the initial feature of the nodes of the hypergraph. Finally, these initial features are used HyperQuery framework.
input to the
In practice, any hypergraph partitioning algorithm can be used to partition the nodes of the hypergraph.
C HYPEREDGE CLASSIFICATION
One neutral choice for our system would be to it to solve hyperedge classification. In such problems, hypergraph H is a tuple (V, E, L) where V is set of nodes; E C 2| is a set of nonempty subsets of called hyperedges; and is a set of labels for hyperedges. Our task is given a hypergraph and labels on small subset of hyperedges, predict labels on the remaining hyperedges.
We evaluate our system on three datasets: Cora, Citeseer, and Pubmed 5 We used 20% of the hyperedges in these datasets for test, 10% for validation and 70% for training (for 20 epochs). Since there are no previous approaches for hyperedge classification, we modified existing methods as baselines for problem:
HyperNetVec Maleki et al. (2022): an unsupervised multi-level approach to generate the repre- sentation of hypergraph. This method an existing embedding system generate initial
12

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Under review as a conference paper at ICLR 2023
embedding and further improve these embeddings using refinement algorithm. This methods gener- ates embeddings for nodes of a hypergraph. We modified this method to also generate embeddings for hyperedges.
node2vec(mean): a random walk based approach to generate representation of a graph in a semi- supervised manner. In order embeddings for the nodes of the hypergraph. We obtain embedding of a hyperedge by performing a mean aggregation the embedding of its nodes.
node2vec, convert our hypergraph to graph and then generate
We used HyperQuery to run these experiments. Table 6 summarizes the result of our experiment. HyperQuery performs the best compared to HyperNet Vec and node2vec. It improves up 2.3% dataset Cora, 18% on Citeseer, and 4% on Pubmed.
Table 5: Real world hypergraph dataset for classification
DATA SET
NODES
HYPEREDGES
TYPE OF DATA
CLASSES
CORA 2,709
1,963
CITATION 7
CITESEER
3,328
2,182
CO-AUTHORSHIP 6
PUBMED
19,717
12,971
CO-AUTHORSHIP
3
Table 6: Hyperedge classification. Accuracy in % and time in seconds.
CORA
CITESEER
PUBMED
ACCURACY
TIME
ACCURACY
TIME
ACCURACY
TIME
HYPERQUERY-MEAN
78.5
10
75.3
12
82.4
25
HYPERNETVEC
76.2
57.1
45
78.1
NODE2VEC-MEAT
76.0
30
57.1
31
74.2
140
13


Reviews:
[{"review_id": "pC4Q9Vue5-N", "reviewer": "Reviewer_dmzc", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The model first generates natural labels by a clustering algorithm and then performs hyperedge prediction by hypergraph convolution.", "summary_of_the_review": "This work identified the shortcomings of the previous work and improved it using simple methods. But the writing is not really satisfactory. The author should revise it significantly to make the work more acceptable to the readers.", "strength_and_weaknesses": "Strength：\n1. The method in this paper shows consistent superiority on experiments with multiple data sets.\n2. The authors identified the shortcomings of their previous work and innovatively improved it through simple methods.\n\nWeaknesses：\n1. The abstract and the introduction section does not state the background of the task, the motivation of the method and where the innovation lies. Instead, the authors define the hypergraph, knowledge hypergraph, and hypergraph prediction tasks in this section, which I think should be explained in the model section. \n2. The captions for Figures 2 and 3 are too long. The description of the model should be placed in the body of the text.\n3. The composition of the pipeline should be further rethought to allow the reader to better understand the model details. \n4. What are equations 1 and 2 for? They are not used in the subsequent objective function Eq. 6.\n5. The logic of the article is not clear, making it difficult for the reader to catch the point. The authors should rethink the organization of their paper to better explain their work.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"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": "Not applicable"}, "extra_text": {}}, {"review_id": "lNxGdecQcJ", "reviewer": "Reviewer_Fuim", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors propose the HyperQuery framework for predicting hyperedges between nodes in hypergraphs. It can also be used to predicted hyperedge types, e.g., in a knowledge hypergraph. Link prediction in hypergraphs is much less studied and more difficult than link prediction in simple graphs. The proposed approach defines an embedding for each hyperedge. These are then aggregated to compute an embedding for each node. They use hypergraph clustering to initialize the embeddings. The authors demonstrate improved empirical results for both knowledge hypergraph completion and hyperedge prediction on several real data sets.", "summary_of_the_review": "This paper addresses an important task, hyperedge prediction in hypergraphs, that has not been very well studied previously. The proposed HyperQuery framework appears sound and may have some novel components, but I am left confused about many elements of this paper. It is quite strange to me that the text in the paper is grammatically sound but lacks clarity in descriptions. Similarly, the figures look good, but I am not sure what several of them are supposed to show.\n\nI think there is a lot of potential in this paper but would not recommend it for publication at this time. If the presentation can be significantly improved, it could become a high quality paper in the future.\n", "strength_and_weaknesses": "Strengths:\n- Considers the task of hyperedge prediction, which is more difficult and less well studied than link prediction in simple graphs.\n- Improvements in accuracy on both prediction tasks is impressive compared to prior methods, including recently proposed neural hyperedge prediction methods HyperSAGNN and NHP.\n\nWeaknesses:\n- Presentation is unclear in many respects. Although the paper is mostly free from grammatical errors, the text and figures are confusing in many aspects. See my questions below.\n- Different elements of the proposed HyperQuery framework seem to be chosen and combined in ad-hoc manner that doesn't provide much insight into why they work.\n- Novelty of different elements in the HyperQuery framework is unclear. \n\nQuestions:\n1. What is Figure 2 supposed to show? On the left pane, I can't tell what the hyperedges are. What are the colored dashed lines supposed to show? Are these the hops in the random walk? What is the right pane supposed to show?\n2. What are the quantities \\#train, \\#valid, and \\#test referring to? They don't appear to map to either the number of entities or relations. Are these counts of hyperedges?\n3. I don't understand the evaluation in Section 6.1. What counts as a hit for hit\\@1 and hit\\@3? Is there a way to give partial credit if HyperQuery is given a query for a subset of entities that have a hyperedge? For example, if a hyperedge exists between $(e_1, e_2, e_3, e_4)$ but the query is for $(e_1, e_2, e_3)$, what is the correct answer, and how is it evaluated?\n\nTypos and minor issues:\n- Figure 1: Prediect -> Predict\n- Section 5.2, first line: varience -> variance\n- Placement of Figure 2 on page 3 seems odd. It is not referenced anywhere around that page, and not until Section 4.1 on page 5. Perhaps Figure 2 should be moved after Figure 3, which is referenced much earlier. Similarly, Figure 5 is in a strange location, showing up before Tables 2-4 despite not being referred to until afterwards.\n- Inconsistent use of the notation $\\mathcal{N}(\\cdot)$. $\\mathcal{N}(v_i)$ is stated to denote the neighborhood of node $v_i$ (incorrectly denoted as $N(v_i)$ in the Figure 3 caption). Then what is $\\mathcal{N}(e)$ for a hyperedge $e$? Is it a union of the neighborhoods for all nodes $v_i \\in e$?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"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."}, "extra_text": {}}, {"review_id": "E00XkoUImhv", "reviewer": "Reviewer_McmT", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a new framework for higher-order link prediction. The paper creates hyperedges embedding (local information) and combines this information with clustering embedding (global information). Both pieces of information were supposed to be combined using an MLP for the final classification process.\n", "summary_of_the_review": "The paper is well-written and proposes a new interesting framework. The results are very interesting, and the work could be publishable. However, the current state of the paper must be improved in terms of clarity and reproducibility. ", "strength_and_weaknesses": "The introduction is well-written and stated the main problem. The related work covers several points of topics and papers. The methodology of the experiment section is also strong. It has several baselines, different problems are considered, and an ablation study is applied to check the importance of each stage of the framework. However, there are several weaknesses that must be improved. \n\nThe most important issue is the clarity of the paper. The paper tries to be general, so different approaches can be considered. This can be observed with the use of functions such as AGG, \\Omega, and others. However, this generality loses the main focus of the paper, and the framework becomes complex (even though it is simple). So, in general, the three sections explaining the main framework must be improved. \n\nThe use of space can also be improved. For example, most of subsection 4.1 can be resumed in a single paragraph. Figure 2 can be explained in a single paragraph, and figure 1 from the appendix could be incorporated into the paper. You can also add the time complexity of the framework (a small part is mentioned in the appendix). This will make the paper stronger. \n\nAnother problem is reproducibility. Unfortunately, several details are omitted. From the use of the clustering algorithm, to all the hyperparameters used in the framework. \n\nMinor comments:\nFigure 1: it says project instead of paper. \nFigure 1 (\"right\" part): it says Prediect\nFigure 5: use a white background, increase the size of the font for the legend, and improve the caption mentioning that it is for a specific experiment.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"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."}, "extra_text": {}}, {"review_id": "DPI3a3UzeAx", "reviewer": "Reviewer_t9m9", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In this paper, the authors study the problem of hyperedge classification in hypergraphs. The authors generalize the idea of GNN to carry out message-passing type methods to alternate between edge and node representations. Experiments are carried out on several datasets with comparison to existing hyperedge classification methods.", "summary_of_the_review": "The authors studied an interesting problem with a natural generalization of GNN to hypergraph as solution. However, both clarity and empirical needs some improvements.", "strength_and_weaknesses": "Strength\n1.The authors study an interesting and practical problem to generalize edge classification to hyperedge with many real-world applications.\n2.The proposed method is a natural generalization to GNN from graph to hyper-graph with alternating node and edge representation learning.\n3.The authors carry out experiments on several datasets with comparison to existing state-of-art methods.\n\nWeakness\n1.The authors should provide more details on the empirical evaluation. First, how important hyper-parameters are set like the number of iteration of message-passing k. Also it would be better to have an experiment on the sensitivity of the parameters. Second, for hyper-edge classification, what is the evaluation protocol e.g. how are the negative samples generated and what is positive to negative ratio etc. In Table 4, does HQ the same as HyperQuery. Also, what is the exact definition of the minimax operation and the bilinear operation used?\n2.Besides hyper-graph based approaches, the authors should compare the proposed method to graph-based methods as well. A neutral choice would be casting the problem as a graph classification problem by flattening all hyper-edges. Comparison to some simple heuristics like graph structure features like number of edges would also be very helpful. \n3.The authors mention the classification of hyperedge types. Seems no experiment is carried out in section 6? Also in section 6.2, why use 70% for test and only use 20% for training?\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"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."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject