Advanced Hypergraph Mining for Web Applications Using Sphere Neural Networks

Abstract

Web-based applications often involve analyzing complex multi-relational data generated by various domains, including social platforms , bibliographic networks, recommendation systems, and e-commerce platforms. Traditional graph-based methods struggle to model interactions beyond simple pairwise relationships, such as higher-order dependencies and the underlying geometric and structural properties of the data. This paper presents a novel application of hyperspherical deep learning to hypergraphs, integrating geometric hypergraph mining with a Sphere Neural Network (SNN) to model and analyze these intricate relationships effectively. Using real-world datasets, including Reddit, DBLP, MovieLens, and Amazon Co-purchase, our framework embeds hypergraphs into hyperspherical spaces, preserving both relational and geometric properties. Experimental results demonstrate that our method significantly improves performance on tasks such as recommendation, co-purchase prediction, and user behavior analysis, outperforming state-of-the-art techniques. This work highlights the potential of integrating geometric hypergraphs and hyperspherical deep learning to advance the analysis of web-based data.

Full text

Advanced Hypergraph Mining for Web Applications Using
Sphere Neural Networks
Zhongtian Sun
zs440@cam.ac.uk
University of Cambridge
Cambridge, UK
University of Oxford
Oxford, UK
University of Kent
Canterbury, UK
Anoushka Harit
University of Cambridge
Cambridge, UK
ah2415@cam.ac.uk
Jongmin Yu
jm.andrew.yu@gmail.com
University of Cambridge
Cambridge, UK
Jingyun Wang
jingyun.wang@durham.ac.uk
Durham University
Durham, UK
Pietro Liò
pl219@cam.ac.uk
University of Cambridge
Cambridge, UK
Abstract
Web-based applications often involve analyzing complex multi-
relational data generated by various domains, including social plat-
forms, bibliographic networks, recommendation systems, and e-
commerce platforms. Traditional graph-based methods struggle
to model interactions beyond simple pairwise relationships, such
as higher-order dependencies and the underlying geometric and
structural properties of the data. This paper presents a novel appli-
cation of hyperspherical deep learning to hypergraphs, integrating
geometric hypergraph mining with a Sphere Neural Network (SNN)
to model and analyze these intricate relationships eectively. Us-
ing real-world datasets, including Reddit, DBLP, MovieLens, and
Amazon Co-purchase, our framework embeds hypergraphs into
hyperspherical spaces, preserving both relational and geometric
properties. Experimental results demonstrate that our method sig-
nicantly improves performance on tasks such as recommendation,
co-purchase prediction, and user behavior analysis, outperforming
state-of-the-art techniques. This work highlights the potential of in-
tegrating geometric hypergraphs and hyperspherical deep learning
to advance the analysis of web-based data.
CCS Concepts
•Computing Methodologies
→
Graph Neural Networks, Hy-
pergraph, Sphere Neural Network.
Keywords
Graph Representation Learning, Recommendation System, Hyper-
graph , Sphere Neural Network
ACM Reference Format:
Zhongtian Sun, Anoushka Harit, Jongmin Yu, Jingyun Wang, and Pietro Liò.
2025. Advanced Hypergraph Mining for Web Applications Using Sphere
This work is licensed under a Creative Commons Attribution Inter-
national 4.0 License.
WWW Companion ’25, Sydney, NSW, Australia
©2025 Copyright held by the owner/author(s).
ACM ISBN 979-8-4007-1331-6/2025/04
https://doi.org/10.1145/3701716.3715577
Neural Networks. In Companion Proceedings of the ACM Web Conference
2025 (WWW Companion ’25), April 28-May 2, 2025, Sydney, NSW, Australia.
ACM, New York, NY, USA, 5 pages. https://doi.org/10.1145/3701716.3715577
1 Introduction
Web-based applications generate vast amounts of complex data,
characterized by multi-relational interactions and higher-order
structures. Examples include user discussions on Reddit [
1
]
1
, aca-
demic collaboration networks on DBLP [
17
]
2
, movie rating patterns
on MovieLens[
6
]
3
, and co-purchase behaviors on Amazon [
9
]
4
.
Traditional graph-based models [
7
,
12
,
14
–
16
,
18
,
20
] often fail to
capture the nuanced relationships and structural complexity inher-
ent in these datasets, limiting their eectiveness in tasks such as
recommendation, behavior prediction, and anomaly detection.
Hypergraphs, which generalize graphs by allowing hyperedges
to connect multiple nodes, provide a more expressive framework for
modeling such relationships [
2
,
5
,
13
]. However, eectively mining
insights from hypergraphs remains a challenge due to their high-
dimensional nature and lack of appropriate embedding techniques.
To address this, we propose a new application of hyperspherical
deep learning to hypergraph analysis, integrating geometric hyper-
graph mining [
11
] with Sphere Neural Networks (SNNs) [
3
,
19
], a
class of neural networks designed for hyperspherical spaces. By
embedding hypergraph structures into a hyperspherical space [
11
],
our approach captures both geometric and relational properties,
enabling robust analysis of web-based datasets. Our contributions
are threefold:
(1)
We introduce a geometric hypergraph mining framework
tailored to web-based data, leveraging the expressive power
of hyperspherical embeddings [10].
(2)
We develop a novel integration of Sphere Neural Networks
[
3
] with hypergraph learning, enhancing higher-order rela-
tionship modeling and extending SNNs beyond traditional
graphs to more complex structures.
1https://zenodo.org/records/3608135
2https://www.kaggle.com/datasets/dheerajmpai/dblp2023
3https://www.kaggle.com/datasets/grouplens/movielens-20m-dataset
4https://snap.stanford.edu/data/amazon-meta.html

WWW Companion ’25, April 28-May 2, 2025, Sydney, NSW, Australia Zhongtian Sun, Anoushka Harit, Jongmin Yu, Jingyun Wang, & Pietro Liò
(3)
We validate our approach on diverse datasets like Reddit [
1
],
DBLP [
17
], MovieLens [
6
], and Amazon Co-purchase [
9
],
demonstrating its superiority in key tasks such as recom-
mendation and link prediction.
2 Related Work
The analysis of web-based data has seen extensive exploration
through graph-based models. Traditional approaches, such as col-
laborative ltering and matrix factorization [
8
], focus on pairwise
relationships but fail to capture higher-order interactions. Hyper-
graphs, which extend graphs by allowing edges to connect multiple
nodes, oer a richer representation of complex data. Hypergraph-
based models have been applied to tasks like recommendation [4]
and community detection [
23
], yet they often struggle with scala-
bility and the ecient encoding of geometric relationships. Recent
advances in geometric deep learning have introduced neural net-
works for non-Euclidean spaces, such as Sphere Neural Networks
(SNNs) [
3
,
19
], which excel at modeling data in hyperspherical
spaces. However, these methods have primarily been applied to
tasks like image classication and molecular structure prediction,
leaving their potential for web-based hypergraph mining under-
explored.Our work bridges these gaps by combining hypergraph
mining with SNNs[
3
] to enable ecient modeling of multirelational
geometric data in web-based applications. Unlike prior methods,
our framework integrates hyperspherical embeddings to preserve
both geometric and relational properties, oering enhanced per-
formance on datasets such as Reddit[
1
], DBLP [
17
], MovieLens[
6
],
and Amazon Co-purchase[9].
3 Method
Our approach combines geometric hypergraph mining [
11
] with
Sphere Neural Networks (SNNs) [
3
] to model and analyze web-
based data eectively.
3.1 Hypergraph Representation
Let the web-based data be represented as a hypergraph
H=(V,E,
X
)
,
where:
(1) V={𝑣1, 𝑣2, . . . , 𝑣𝑁}is the set of 𝑁nodes.
(2) E={𝑒1, 𝑒2, . . . , 𝑒𝑀}is the set of 𝑀hyperedges.
(3)
X
∈R𝑁×𝐹
is the node feature matrix, where
𝐹
is the dimen-
sionality of the input features.
Each hyperedge
𝑒𝑘
connects a subset of nodes
V
𝑘⊆ V
. The inci-
dence matrix H∈R𝑁×𝑀encodes this relationship:
𝐻𝑖,𝑘 =(1if 𝑣𝑖∈ V
𝑘
0otherwise
3.2 Hyperspherical Embedding
To map the hypergraph to a geometric space, we embed nodes
and hyperedges into a hyperspherical manifold. The embedding
function
𝜙
:
V ∪ E → S𝑑
projects nodes and hyperedges onto the
𝑑-dimensional unit sphere:
𝜙(𝑣𝑖) ∈ S𝑑and 𝜙(𝑒𝑘) ∈ S𝑑,where S𝑑={x∈R𝑑+1:∥x∥2=1}.
(1)
The embeddings are optimized to minimize the hyperspherical
distortion while preserving relational and geometric properties.
This is achieved via:
Lembed =
(𝑖, 𝑗 )∈E
𝑤𝑖 𝑗 ·𝜙(𝑣𝑖)−𝜙𝑣𝑗2
2+𝛽·
𝑖∈ V ∥𝜙(𝑣𝑖) ∥2
2−12,
(2)
(𝑖, 𝑗 ) ∈ E
is a connected node pair with weight
𝑤𝑖 𝑗 .𝜙 (𝑣𝑖)
is the
hyperspherical embedding,
𝜙(𝑣𝑖)−𝜙𝑣𝑗2
2
enforces proximity,
𝛽
regulates constraints, and
∥𝜙(𝑣𝑖)∥2
2−
1penalizes deviations from
the unit sphere.
3.3 Sphere Neural Network (SNN)
The SNN operates on hyperspherical embeddings to propagate and
aggregate features. It consists of the following layers:
(1)
Spherical Convolution: The spherical convolution layer ag-
gregates features along hyperedges using:
h(𝑙+1)
𝑣=ReLU ©«
𝑒𝑘∈ N (𝑣)
1
|V
𝑘|
𝑣𝑗∈ V
𝑘
W(𝑙)h(𝑙)
𝑣𝑗ª®¬,(3)
where h
(𝑙)
𝑣∈R𝑑
is the feature of node
𝑣
at layer
𝑙, N (𝑣)
is
the set of hyperedges containing
𝑣
, and W
(𝑙)
is the trainable
weight matrix.
(2)
Spherical Attention Mechanism: An attention mechanism
assigns importance scores to hyperedges
𝛼𝑘=
exp a⊤·concat h𝑣𝑖,h𝑒𝑘
Í𝑘′exp a⊤·concat h𝑣𝑖,h𝑒𝑘′,(4)
where ais a learnable parameter vector. The attention scores
𝛼𝑘are used to weight the hyperedge contributions.
3.4 Task-Specic Objectives
We formulate task-specic loss functions tailored to web-based
applications:
(1)
Recommendation: For link prediction (e.g., co-purchase or
ratings), we maximize the similarity between connected
nodes on the hypersphere:
L𝑟𝑒𝑐 =−
(𝑖, 𝑗 )∈E+
log 𝜎𝜙(𝑣𝑖)⊤𝜙(𝑣𝑗)−
(𝑖, 𝑗 )∈E−
log 1−𝜎𝜙(𝑣𝑖)⊤𝜙(𝑣𝑗).
(5)
where
E+
and
E−
are the positive and negative edges, respec-
tively, and 𝜎is the sigmoid function.
(2)
Clustering: For community detection, we minimize the intra-
cluster variance while maximizing inter-cluster separation:
Lclust =
𝐶
1
|𝐶|
𝑣𝑖,𝑣𝑗∈𝐶𝜙(𝑣𝑖)−𝜙𝑣𝑗2
2−𝜆
𝐶,𝐶′
∥c𝐶−c𝐶′∥2
2,
(6)
where c𝐶is the cluster centroid, and 𝜆balances intra-cluster com-
pactness and inter-cluster separation.
3.5 Overall Optimization
The total loss function combines embedding, task-specic, and
regularization terms:
L=Lembed +𝛾Ltask +𝜆Lreg (7)

Advanced Hypergraph Mining for Web Applications Using Sphere Neural Networks WWW Companion ’25, April 28-May 2, 2025, Sydney, NSW, Australia
where
Lembed
preserves relational and geometric properties by
keeping connected nodes close and enforcing the hyperspherical
constraint;
Ltask
optimizes task-specic objectives like link pre-
diction or clustering; and
Lreg
prevents overtting and improves
stability by constraining model parameters. The hyperparameters
𝛾
and
𝜆
(same as used in equation 6) balance task-specic learning
and regularization for optimal generalization.
4 Experiments
We evaluate the proposed HyperSNN framework on four widely
used benchmark hypergraph-structured web datasets, including
Reddit [
1
], DBLP [
17
], MovieLens [
6
], and Amazon Co-Purchase [
9
],
by comparing it with state-of-the-art baselines and conducting an
ablation study to analyze the eectiveness of its components.
4.1 Experiment Setup
4.1.1 Datasets and Baselines. Reddit and DBLP focus on link pre-
diction tasks, while MovieLens and Amazon Co-Purchase target
recommendation and co-purchase prediction tasks. We compare Hy-
perSNN with baselines, including Graph Convolutional Networks
(GCN) [
7
], Graph Attention Networks (GAT) [
18
], Hypergraph GCN
[21], and a Multi-Layer Perceptron (MLP) [22].
4.1.2 Implementation Details. Node features are normalized for
numerical stability and faster convergence. Uniform weights are
assigned to hyperedges for consistency across datasets, and the hy-
pergraph is stored as a sparse incidence matrix to optimize memory
and computation for large-scale data. Models are trained for 100
epochs using the Adam optimizer with a learning rate of 0.01 and
a weight decay of 10
−4
for regularization. Experiments are con-
ducted on an NVIDIA GeForce 2080 Ti GPU and evaluated on Area
Under the Curve (AUC), Precision@10, and Mean Reciprocal Rank
(overMRR), with results averaged over ve runs using dierent
random seeds to ensure statistical robustness.
4.2 Results
We evaluate HyperSNN across four datasets (Reddit, DBLP, Movie-
Lens, Amazon Co-Purchase), selecting metrics suited to each task.
For link prediction, AUC measures the ability to distinguish correct
links, while MRR evaluates ranking quality. For recommendation,
P@10 assesses top-10 relevance, and MRR ensures accurate ranking.
These task-specic metrics provide a fair and meaningful evaluation.
The following sections analyze performance, compare baselines,
and present ablation insights.
4.2.1 Link Prediction Task. We present the results of link predic-
tion experiments on Reddit [
1
] and DBLP [
17
] datasets in Table 1.
HyperSNN achieves the highest AUC scores, improving by 6.0% and
5.0% on Reddit and DBLP, respectively, compared to the strongest
baseline. AUC evaluates the model’s ability to rank positive links
higher than negative ones, making it a key metric for link prediction.
Furthermore, HyperSNN exhibits low standard deviation across
runs, highlighting its stability and robustness in capturing complex
hypergraph structures.
Table 1: Link Prediction Results (AUC on Reddit and DBLP)
Model Reddit DBLP
Mean AUC (%) Std Dev (%) Mean AUC (%) Std Dev (%)
GCN 82.0 2.1 80.0 2.3
GAT 84.0 2.0 83.0 2.4
HyperGCN 85.0 1.9 84.0 2.2
MLP 73.0 3.5 72.0 3.6
HyperSNN 91.0 1.7 89.0 1.8
Figure 1: Model Performance for Link Prediction Task
These results highlight HyperSNN’s eectiveness in modeling
higher-order interactions within hypergraphs. Although traditional
models such as GCN [
7
] and GAT [
18
] leverage neighborhood
aggregation, they struggle to capture the geometric and relational
complexity that HyperSNN excels at.
4.2.2 Recommendation and Co-Purchase Prediction Tasks. We eval-
uate HyperSNN on MovieLens[
6
] and Amazon Co-Purchase datasets[
9
]
for recommendation and co-purchase prediction tasks. As shown in
Table 2, HyperSNN outperforms all baselines in both Precision@10,
which measures the relevance of the top 10 recommendations, and
MRR, which evaluates the quality of the rankings. This demon-
strates HyperSNN’s ability to generate and rank relevant recom-
mendations eectively for real-world applications.
Table 2: Recommendation Results (Precision@10 on Movie-
Lens and MRR on Amazon)
Model MovieLens (Precision@10) Amazon (MRR)
Mean (%) Std Dev (%) Mean (%) Std Dev (%)
GCN 76.0 2.5 70.0 2.7
GAT 78.0 2.3 72.0 2.5
HyperGCN 79.0 2.0 73.0 2.2
MLP 65.0 3.4 60.0 3.5
HyperSNN 87.0 1.8 81.0 1.9

WWW Companion ’25, April 28-May 2, 2025, Sydney, NSW, Australia Zhongtian Sun, Anoushka Harit, Jongmin Yu, Jingyun Wang, & Pietro Liò
Figure 2: Model Performance for Recommendation and Co-
Purchase Prediction Tasks
These results demonstrate that the hyperspherical embeddings
learned by HyperSNN provide superior representation power for
user-item and product interactions.
4.3 Ablation Study
We perform an ablation study to assess the contribution of key
components in HyperSNN by systematically removing the atten-
tion mechanism and hyperspherical embeddings. Table 3 and Fig 3
shows that removing the attention mechanism reduces the AUC,
demonstrating its importance in assigning relevance to hyperedges.
Table 3: Ablation Study Results Across All Datasets
Model Variant Reddit DBLP MovieLens Amazon
(AUC) (AUC) (P@10) (MRR)
Full Model 0.91 0.89 0.87 0.81
Without Attention 0.88 0.85 0.84 0.78
Without Hyperspherical 0.82 0.80 0.79 0.73
Without Both 0.79 0.77 0.75 0.70
Figure 3: Ablation Study for HyperSNN
Similarly, replacing hyperspherical embeddings with Euclidean
embeddings results in a signicant drop in performance, highlight-
ing the necessity of geometric representations for capturing re-
lational structures. These results conrm the critical role of both
components in HyperSNN’s success.
5 Discussion
HyperSNN achieves superior performance across all datasets by
leveraging hyperspherical embeddings to capture geometric re-
lationships and an attention mechanism to prioritize critical hy-
peredges. The ablation study highlights the importance of these
components, with signicant performance drops when either is
removed. The spherical convolution layer ensures eective feature
aggregation, preserving the relational and geometric properties of
hypergraphs. The model’s scalability is evident from its ecient
handling of large datasets like Amazon Co-Purchase [
9
], thanks to
sparse representations and batch processing. However, its reliance
on hyperspherical embeddings and attention mechanisms increases
memory usage. This trade-o is oset by its ability to consistently
deliver stable and accurate results, as evidenced by low standard de-
viations across runs. HyperSNN’s success underscores the value of
integrating geometric learning with hypergraph structures, paving
the way for further advancements in this domain.
6 Conclusion
We introduced HyperSNN, a novel framework that integrates hy-
perspherical embeddings and attention mechanisms to eectively
hypergraph modeling. By leveraging geometric representations and
dynamic edge weighting, HyperSNN achieves strong performance
in link prediction, recommendation and co-purchase prediction. Ex-
periments on Reddit, DBLP, MovieLens, and Amazon Co-Purchase
datasets demonstrate its superiority over state-of-the-art baselines,
achieving signicant improvements in AUC, Precision@10, and
MRR.
The ablation study conrms the importance of hyperspherical
embeddings and attention mechanisms, with performance drops
observed when either is removed. HyperSNN also scales eciently
on large datasets using sparse representations, though its memory
requirements remain a limitation. Future work can focus on improv-
ing memory eciency, enhancing robustness to noisy data, and
extending HyperSNN to dynamic hypergraphs, further expanding
its applicability in real-world scenarios.
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