H 2 O GNN: Hypergraph-based heterophily-aware neural network for service recommendation

Abstract

Service recommendation systems play a crucial role in delivering personalized user experiences across various domains. However, capturing the heterophily patterns and the multi-dimensional nature of user-service item interactions poses significant challenges. To address these challenges, we propose a service recommendation model named $H^{2} O$ GNN (Hypergraph-based Heterophily-Aware Neural Network for Service Recommendation), which incorporates three key components: (1) a hypergraph disentangled contrast module that explicitly separates homophily and heterophily signals within hyperedges, enabling more accurate feature representation; (2) a heterophily-aware attention mechanism that dynamically adjusts information propagation weights based on node feature differences, enhancing interaction efficiency between heterophilic nodes; and (3) a dynamic multi-interest learning module that disentangles users’ latent preferences into multiple interest vectors and activates relevant interests according to target service items, achieving fine-grained modeling of cross-category preferences. Extensive experiments on Steam, MovieLens, and Yelp datasets demonstrate the effectiveness of $H^{2} O$ GNN, with its Recall@20 metric outperforming the state-of-the-art baseline (HMGSR) by approximately 14.1% on Steam, 12.0% on MovieLens, and 13.9% on Yelp—and is consistently superior to the latest models across all datasets.

Keywords

Service recommendation hypergraph heterophily graph neural networks multi-interest learning

1. Introduction

In the era of explosive growth in digital services, service recommendation systems serve as the core hub connecting users with massive service items, aiming to precisely capture users’ dynamic preferences and model complex interaction relationships to improve service recommendation accuracy. By filtering vast amounts of content, this approach has become critical for enhancing user experiences in diverse applications, such as social network platforms,¹ streaming services,², and online shopping websites.³

The rise of graph neural networks (GNNs) has brought revolutionary advancements to service recommendation systems, effectively modeling implicit collaborative signals by capturing the topological structure of user-service item interaction graphs.^4–6 Early GNN-based collaborative filtering (CF) models, such as LightGCN⁷ and UltraGCN,⁸ significantly improved service recommendation accuracy by aggregating neighbor node features through graph convolution operations.

However, these models inherently rely on pairwise interaction modeling, which limits their ability to capture only direct associations between users and service items. As a result, they face significant challenges in modeling complex, high-order relationships. Specifically, they struggle to effectively represent semantic correlations that arise from multiple users interacting with the same service item simultaneously, or from users engaging with multiple heterophilic (i.e., dissimilar) service items. For instance, discovering latent cross-category interests—such as users who simultaneously prefer both “technology information” and “outdoor equipment”—or identifying cross-group interaction patterns—such as users from different age groups collectively engaging with a “health management application”—requires modeling beyond pairwise interactions. Unfortunately, the traditional binary edge-based modeling approach, which only captures point-wise user-item interactions, is insufficient for capturing such nuanced, high-order correlations. This limitation results in service recommendations being confined to a single dimension and lacking deep insights into users’ diverse needs and group commonalities.

To overcome the representational bottleneck of binary interactions in service recommendation, hypergraphs have been introduced into relevant frameworks^9–11 — their core advantage lies in naturally supporting group-level interaction modeling via hyperedges that connect multiple nodes (e.g., a hyperedge linking one user to all service items they interact with, or one service item to all users who engage with it). Typical hypergraph-based methods, such as DHCF¹² and SHT,¹³ have demonstrated strengths in high-order relationship modeling: DHCF adopts a two-pass hypergraph neural network to separately learn user and service item embeddings, while SHT integrates global collaborative signals through hypergraph transformation and attention strategies. However, both models lack explicit mechanisms for heterophily modeling, leading to critical limitations in capturing real-world diverse interactions:DHCF treats all nodes within a hyperedge as homogeneous, failing to distinguish cross-category signals. For instance, it cannot preserve a user’s simultaneous preference for “technology information services” and “outdoor equipment services,” resulting in the loss of cross-type interaction information. SHT perpetuates the “homophily assumption” of traditional GNNs, assuming nodes of the same type (e.g., same-category service items, users with similar demographic features) have similar embeddings. It thus cannot adjust information propagation for heterophilic nodes — such as when users from different age groups collectively select a “health management app” — and overlooks the unique value of dissimilar nodes in hyperedges.In summary, existing hypergraph recommendation models (e.g., DHCF, SHT) excel at high-order interaction modeling but uniformly neglect the prevalent heterophily interactions in practical scenarios — i.e., the phenomenon where heterophilic nodes (cross-category service items, users with dissimilar features) are connected by the same hyperedge. This oversight directly limits their ability to model users’ diverse preferences and complex service correlations.

Heterophily refers to the phenomenon where linked nodes have dissimilar features and different class labels,^14,15 As illustrated in Figure 1. In contrast to hypergraph models that ignore heterophily, recent heterophily-aware methods (e.g., Hetero $^{2}$ Net¹⁶ HGAT¹⁷) have been proposed to address dissimilar node interactions in graph learning. By definition, heterophily refers to the phenomenon where linked nodes exhibit dissimilar features and different class labels (14; 15) — a pattern widespread in service recommendation, such as: A user interacting with game services of action, strategy, and adventure genres simultaneously (these cross-category services have distinct features, e.g., action games emphasizing operation speed vs. strategy games focusing on tactical planning);A “health management app” co-selected by users from distinct age groups (45–54, 18–24, 35–44 years old), who have divergent consumption preferences and behavioral patterns. These heterophily-aware models have designed targeted mechanisms to handle such patterns:Hetero2Net disentangles homophily and heterophily signals via masked meta-path prediction, focusing on semantic correlations among diverse node/edge types;HGAT adjusts information propagation weights through heterophilic attention, adapting to feature differences between linked nodes.However, a critical limitation of these methods is their design for traditional heterophilic graphs (with pairwise edges) rather than hypergraphs. They can only capture binary node associations (e.g., one user linked to one service item) and fail to adapt to the high-order multi-node structure of hyperedges — for example, a single hyperedge connecting one user to 5 cross-category services. This structural mismatch means even state-of-the-art heterophily-aware models cannot capture the multi-node semantic correlations in hypergraphs, making them unable to be directly applied to hypergraph-based service recommendation.

Figure 1.

Example of heterophilic pattern in user and service item hypergraphs.

In real-world service recommendation scenarios, users frequently interact with heterophilic service items (e.g., browsing movies, games, and educational services simultaneously), requiring models to capture both the tight correlations among homogeneous service items, the differential features of heterophilic service items, and the diverse latent preferences behind these interactions. However, three types of existing models fall short here: First, existing hypergraph convolutional networks (HGCNs)¹⁸ rely on deeply stacked layers to aggregate multi-hop neighbor information, which triggers severe over-smoothing issues in strongly heterophilous scenarios—feature disparities of heterophilic nodes are progressively diluted, diminishing inter-layer representation discriminability; Second, hypergraph models like DHCF and SHT have path dependency on “homophily signals”, so they cannot dynamically adjust information propagation weights for heterophilic nodes (e.g., users of different age groups co-interacting with a service item), exacerbating the modeling deficiency of heterophilous patterns¹⁹; Third, multi-interest models like ComiRec (Cen et al., 2020)—which generate multiple interest embeddings to capture cross-category preferences—are based on sequential data or bipartite graphs, not hypergraphs, so they cannot integrate high-order interaction semantics (e.g., latent interests reflected by a user’s co-interaction with “movies + games + education” services) into interest modeling. These limitations make it challenging to capture all relevant signals (e.g., shared preferences, cross-genre interests) and irrelevant signals (e.g., irrelevant demographic overlaps), which is a key motivation for developing $H^{2} O$ GNN to effectively handle complex service recommendation settings.

To address the above limitations, this paper proposes the $H^{2} O$ GNN (Hypergraph based Heterophily-Aware Neural Network for Service Recommendation) model, which explicitly separates homophily and heterophily representations through Hypergraph Disentangled Contrastive Module (DHCM), enhances interaction weights for heterophilic nodes via a Heterophily-Aware Attention Mechanism, and decouples users’ diverse preferences through dynamic multi-interest learning. These designs break through traditional hypergraph models’ reliance on homophily and systematically integrate heterophily-aware mechanisms into high-order interaction modeling for the first time, providing a new solution for accurate service recommendation in strongly heterophilous scenarios.

The main contributions of this work are summarized as follows:

We propose a service recommendation model named $H^{2} O$ GNN. In this model, we introduce “Hypergraph Homophily Ratio” to quantify the proportion of homophilic node pairs within hyperedges. This metric reveals the inherent limitations of traditional models when applied to heterophilic scenarios. Additionally, we propose the “Disentangled Hypergraph Contrastive Module (DHCM)” to disentangle homophilic and heterophilic signals into separate feature representations. By breaking homophily assumptions, our approach enables more effective modeling of complex high-order interactions in heterophilic scenarios.

We propose a heterophily-aware attention mechanism in $H^{2} O$ GNN that dynamically quantifies feature differences between nodes via a complementary form of cosine similarity. This allows the model to adaptively adjust attention weights, thereby enhancing information propagation for heterophilic node pairs.

We design a dynamic multi-interest learning module that generates multi-interest embeddings by disentangled users’ latent interest spaces and dynamically activates relevant interests based on target service item features, enabling fine-grained modeling of users’ cross-category preferences.

The remainder of this paper is organized as follows: Section 2 introduces the related work. Section 3 gives problem statement and basic definitions. Section 4 presents empirical observations of the challenges of heterophily on service datasets. Section 5 provides a detailed description of $H^{2} O$ GNN. Section 6 presents experimental results and analysis. Section 7 concludes the paper.

2. Related work

2.1. Traditional collaborative filtering and graph neural network-based service recommendation

The core objective of service recommendation systems is to capture dynamic preferences by modeling user-service item interactions. Early approaches such as matrix factorization (MF)^20–22 and neighborhood-based collaborative filtering (CF)^23,24 learn user and service item embeddings from explicit or implicit feedback but struggle to capture high-order structural information. With the development of graph neural networks (GNNs), graph-based collaborative filtering models (e.g., LightGCN,⁷ NGCF²⁵) have significantly improved service recommendation accuracy by aggregating neighbor node features through graph convolutions and encoding interaction structures into node representations. These models rely on the edge structure of user-service item bipartite graphs and focus on pairwise interaction modeling, but they are limited in handling complex multi-way relationships (e.g., multiple users interacting with the same service item or users engaging with multi-category service items), making it difficult to mine implicit high-order collaborative signals.

2.2. Hypergraph neural networks and high-Order interaction modeling

To overcome the representational bottleneck of binary interactions, hypergraphs have been introduced into the service recommendation field due to their ability to model group-level interactions. Hypergraphs connect multiple nodes through hyperedges, naturally capturing diverse associations between users and service items (e.g., service item sets interacted with by a user or user groups associated with a service item). Typical methods like SHT,¹³ which integrates global collaborative signals via hypergraph transformation and attention mechanisms, and DHCF,¹² which uses a two-pass hypergraph neural network to separate user and service item embeddings, have demonstrated advantages in high-order relationship modeling. However, existing hypergraph models generally adhere to the ‘homophily assumption’—assuming that homogeneous nodes have similar embeddings-while ignoring the prevalent heterophily interactions in real-world scenarios, where heterophilic nodes (e.g., cross-category service items, users of different age groups) are connected by hyperedges. This neglect of heterophily signals leads to semantic gaps in modeling complex interaction patterns.

2.3. Heterophily learning

Heterophily refers to the tendency of nodes with different attributes or types to form connections, has gained increasing attention in graph learning.^14,15 Traditional GNNs rely on homophily signals, leading to significant performance degradation on heterophilous graphs. To address this, heterophily-aware methods have been proposed, such as Hetero $^{2}$ Net,¹⁶ which disentangle homophily and heterophily signals via masked meta-path prediction, and HGAT,¹⁷ which introduces heterophilic attention mechanisms to adjust information propagation weights across node types. However, these works primarily focus on heterophilic graphs (with diverse node/edge types) rather than hypergraph structures and do not consider heterophily quantification or signal disentangling in high-order interactions. In service recommendation scenarios, heterophily within hyperedges manifests not only as node-type differences but also as multi-dimensional feature disparities (e.g., service item categories, user age groups), making existing methods difficult to directly apply.

2.4. Multi-Interest modeling, dynamic preference disentangling and others

User preferences are often multi-faceted, spanning multiple categories or domains. Dynamic multi-interest models (e.g., DMI-GNN,²⁶ ComiRec²⁷) generate multiple interest embeddings via attention mechanisms or disentangling networks and activate relevant interests based on target service items, effectively capturing cross-category preferences. However, most existing multi-interest methods are based on sequential data or bipartite graph structures and do not integrate with hypergraph-based high-order interaction modeling, leading to neglect of high-order semantics in user-service item interactions (e.g., latent interest dimensions reflected by multiple service items) during interest disentangling.¹⁵ Additionally, these methods do not explicitly address the impact of heterophily on interest activation—traditional interest matching mechanisms may fail when target service items are heterogeneous from users’ historical interaction service items.

To address historical interaction scarcity in cold-start recommendation,²⁸ researchers have explored four complementary research threads: Content Features^29–31: exploits inherent user/item descriptive attributes (e.g., profiles, descriptions) with data-incomplete or efficient learning to model cold-start entities; Graph Relations^32–34: enrich cold-start entities’ context via interaction graph enhancement, heterogeneous/attribute/knowledge graph extension, or graph aggregator optimization; Domain Information^35–37: borrow information from related, data-rich domains via transfer, alignment, or domain-invariant representation learning; World Knowledge from LLMs^38–40: prompt or fine-tune large language models to inject external commonsense and semantic priors for previously unseen users or items. Our work falls within the graph-relations thread: we leverage higher-order structures to alleviate cold-start scarcity, and we explicitly integrate heterophily modeling—a perspective still largely unexplored in this line of research.

Multimodal recommendation, a prominent direction in recommender systems, effectively enhances performance via diverse modalities. It captures latent cross-modal correlations and recovers complementary information unavailable to unimodal or implicit interaction-based methods. Notable advancements have been made recently with innovative frameworks.^41,42 Yet a key challenge remains—multimodal data is not always accessible in practice, and this constitutes a research direction we will consider in future work.

3. Problem formulation

In this section, we present the preliminaries and problem statement. Specifically, we first define the user-service item interactions and user-service item hypergraphs, followed by the definitions of heterophily patterns and homophily metrics. Then we give the definition of the proposed problem.

3.1. Service interaction graph

In service recommendation scenarios, the interaction graph for service recommendation serves as a core data structure for modeling explicit associations between users and service items. Typically, it is a bipartite graph $G = (U, V, E)$ , where $U$ and $V$ denote the sets of users and service items, respectively, and $E$ is the set of edges representing interactions (e.g., clicks, purchases, or ratings) between users and service items. Each edge is denoted as $(u, v) \in E$ .

3.2. User-Service item hypergraphs

The hypergraphs in this paper are divided into user hypergraphs and service item hypergraphs:

User Hypergraph $H_{u} = (U, ε_{u})$ focuses on relationships between users. Here, $U$ is the set of user nodes, and $ε_{u}$ is the set of hyperedges. Each hyperedge $e \in ε_{u}$ connects a group of users with identical interaction patterns, such as users engaging with the same service item or exhibiting similar preferences.

Service Item Hypergraph $H_{v} = (V, ε_{v})$ focuses on relationships between service items. Here, $V$ represents the set of service item nodes, and $ε_{v}$ is the set of hyperedges. Each hyperedge $e \in ε_{v}$ connects a subset of service items co-interacted with the same user or user group. This structure supports modeling co-occurring service items (e.g., service items frequently purchased together or shared in playlists) and describes their interdependencies in a higher-order manner.

Hyperedge construction adheres to the core theoretical principles of maintaining the consistency of high-order interaction semantics and preserving heterophily signals, and is divided into two types: user hyperedges and service hyperedges. User hyperedges are built based on the collaborative filtering assumption that “users with similar interaction patterns share consistent preference” and the principle of “heterophily tolerance”. They are formed by grouping users who meet either of the following criteria: a relatively high similarity in their service category preference distributions, or co-interaction with several types of homophily services. For example, consider a user Alice, who has interacted with services such as book borrowing and offline restaurant reservations, and a user Bob, who has interacted with services like library resource access and chain café bookings. Although there are differences in their service usage scenarios—specifically, Alice may be more inclined to offline consumption while Bob prefers online consumption, reflecting a certain degree of heterophily—their overall interaction preference distributions show high similarity, and they have also co-interacted with several homophily services under the “daily life service” category. Thus, Alice and Bob are incorporated into the same user hyperedge—this not only captures the commonalities in their preferences but also preserves the heterophily-related differences between them. Service hyperedges follow the logic of “explicit preservation of heterophily”, grouping all services interacted with by a single user into a single hyperedge. Taking the Alice mentioned above as an example, all services she has interacted with are integrated into a single service hyperedge. within which homophilous and heterophilous services coexist. This coexistence provides essential signals for subsequent heterophily modeling.

3.3. Heterophily in hypergraphs

In the context of user-service item hypergraphs, heterophily manifests as users or service items with disparate features being interconnected via the same hyperedge. Unlike binary interaction graphs, hypergraphs often exhibit heterophily patterns. This is because they are capable of modeling diverse high-order relationships, grouping users or service items with distinct characteristics within the same hyperedge based on shared interactions or contexts. Identifying heterophily patterns is of paramount importance for enhancing service recommendation accuracy. By discerning these patterns, models can distinguish between varied and contrasting relationships within the hypergraph structure. This enables a more nuanced understanding of user-service item interactions, facilitating the provision of more targeted and precise service recommendations.

3.4. Hypergraph homophily ratio

Homophily metrics quantify the correlation between graph structural adjacency and node attributes/labels, which is a core basis for evaluating the applicability of graph models to specific scenarios. Traditional homophily metrics are primarily designed for pairwise graphs (with binary edges connecting only two nodes) and have been widely adopted in homogeneous graph learning as Formula 1:

\begin{aligned} H_{e d g e} (G) = \frac{1}{| E |} \sum_{(u, v) \in E} I (y_{u} = y_{v}) \end{aligned}

(1)

This metric only characterizes pairwise edge-level homophily. Node-level homophily (equation (??)) averages the label agreement over each node’s immediate neighbours, but still collapses relationships into pairwise comparisons:

\begin{aligned} H_{n o d e} (G) = \frac{1}{| V |} \sum_{u \in V} \frac{\sum_{v \in N (u)} I (y_{u} = y_{v})}{| N (u) |} \end{aligned}

(2)

In service-recommendation hypergraphs, a single hyperedge can simultaneously connect users who prefer “technology news,” “outdoor equipment,” and “health management.” Because the traditional metrics never inspect the label composition of an entire multi-node group, they systematically underestimate or overestimate the true degree of homophily and overlook the high-order semantic cues needed to model cross-category preferences. We therefore require a measure that evaluates label consistency within each hyperedge as a whole rather than merely between node pairs.

Thus, to quantitatively analyze heterophily patterns in hypergraphs, we define the Hypergraph Homophily Ratio metric $H (G)$ , which measures the proportion of homophilic node pairs within hyperedges. This metric extends the traditional graph homophily definition to accommodate the high-order interaction structures of user-service item hypergraphs:

\begin{aligned} H (G) = \frac{1}{| U |} \sum_{u \in U} H (U) = \frac{1}{| U |} \sum_{u \in U} \frac{\sum_{v_{i}, v_{j} \in E_{u}^{H_{v}}} I (y_{v_{i}} = y_{v_{j}})}{C_{| E_{u}^{H_{v}} |}^{2}}, \end{aligned}

(3)

Where $E_{u}^{(H_{v})}$ denotes the set of hyperedges composed of service items interacting with user $u$ in the service hypergraph $H_{v}$ . Let $I$ be an indicator function such that $I = 1$ if service items $v_{i}$ and $v_{j}$ belong to the same category, and $I = 0$ otherwise. The notation $C_{| E_{u}^{(H_{v})} |}^{2}$ represents the number of all possible node pairs in the hyperedge set $E_{u}^{(H_{v})}$ .A higher $H (G)$ indicates stronger homophily, while a lower $H (G)$ signifies stronger heterophily.

3.5. Problem definition

Let a service interaction graph $G = (U, V, E)$ be a set of users $(U)$ , a set of service items $(V)$ , and their historical interaction relationships $(E)$ , suppose we have a target user $u_{i}$ and a set of service items $V_{u_{i}}$ which $u_{i}$ has invoked. In service recommendation scenarios, heterophily is prevalent: target service items may exhibit significant attribute divergence from users’ historically interacted service items within $V_{u_{i}}$ . Meanwhile, users typically harbor multiple latent interests. Ours goal is to recommend the top $k$ service items from $V ∖ V_{u_{i}}$ that should be most likely to be interacted with by $u_{i}$ .

4. Empirical observations

To deeply investigate the intrinsic correlation between hypergraph homophily and the performance of graph neural networks (GNNs), we conducted an empirical study to analyze the effects of different homophily levels on the performance of service recommendation models. Specifically, we want to empirically examine whether the recommendation performance of classical GNN models degrades as the the degree of heterophily in the underlying user-service interaction patterns increases. To address this, we select Steam and MovieLens (the details of these two datasets will be introduced in Section 6.) as the datasets and employ a 2-layer GCN⁴³ with ReLU activation and a hidden size of 64 as the baseline model. Additionally, two widely used metrics for service recommendation, Recall@K and NDCG@K (details of these metrics will also be introduced in Section 6) are selected to evaluate the recommendation performance. The research results are presented in Table 1, from which the following observations can be made:

Table 1.
The recommendation result of GCN. H(G) denotes the hypergraph homophily ratio in sec 3.

Overall GCN Overall GCN

Dataset $H (G)$ (%) Recall@20 NDCG@20

Steam 37.45 0.3158 0.1246

48.13 0.3284 0.1356

71.36 0.5942 0.3141

87.73 0.6433 0.3245

MovieLens 42.19 0.4001 0.2844

55.54 0.4100 0.2889

62.93 0.5833 0.3345

74.85 0.6045 0.3469

		Overall GCN	Overall GCN
Steam	37.45	0.3158	0.1246
	48.13	0.3284	0.1356
	71.36	0.5942	0.3141
	87.73	0.6433	0.3245
MovieLens	42.19	0.4001	0.2844
	55.54	0.4100	0.2889
	62.93	0.5833	0.3345
	74.85	0.6045	0.3469

Positive Correlation between Homophily and Performance. As the $H (G)$ increases (heterophily decreases), the model performance improves significantly. Both the Steam and MovieLens datasets show that with stronger homophily, the GCN model achieves notable improvements in service recommendation tasks. This indicates that hypergraph structures with higher homophily are more conducive for traditional GCN to capture node similarity and enhance service recommendation accuracy.

Challenges of Heterophily. On the Steam and MovieLens datasets with low $H (G)$ values, GCN performance is limited, reflecting the shortcomings of traditional GNNs in strongly heterophilous scenarios—their excessive reliance on homophily signals makes it difficult to effectively utilize interaction information from heterophilic nodes.

These two findings demonstrate that the hypergraph homophily ratio significantly impacts the service recommendation performance of graph convolutional networks (GCN): hypergraph structures with stronger homophily more efficiently support traditional GCN in capturing node similarity, while performance degradation of GCN in strongly heterophilous scenarios exposes their reliance on homophily signals and insufficient modeling of heterophilous interactions. These results inspire us that the limitations of traditional GNNs in heterophilous hypergraphs fundamentally stem from the lack of mechanisms to process heterophilous signals in high-order interactions, urgently requiring the design of targeted mechanisms to explicitly capture heterophily patterns.

5. Methodology

In this section, we provide a detailed analysis of our proposed $H^{2} O$ GNN model. As illustrated in Figure 2, the overall architecture of our model comprises three core modules: the Heterophily-Aware Attention Mechanism, the Hypergraph Disentangling Contrastive Module (DHCM), and the Dynamic Multi-Interest Learning Module. These modules work synergistically to capture high-order interactions and disentangle heterophily signals, enabling accurate modeling of user preferences and service item correlations in heterophilous scenarios.

Figure 2.

The main modules of the proposed $H^{2} O$ GNN.

5.1. Heterophily-Aware attention mechanism

Given the initial feature embeddings of user node $u$ and service item node $v$ as $x_{u}, x_{v} \in R^{d}$ , where $d$ denotes the dimension of input features, the linear transformation layer generates a new set of node features $h_{u}, h_{v} \in R^{d^{'}}$ through a transformation weight matrix $W_{u}, W_{v} \in R^{d \times d^{'}}$ , with $d^{'}$ being the dimension of the projected features.

\begin{aligned} h_{u} = x_{u} W_{u}, h_{v} = x_{v} W_{v}, \end{aligned}

(4)

After equation (4), the features of the input nodes are enhanced to better adapt to the following tasks.

Building upon traditional graph attention mechanisms (e.g., GAT⁴⁴), to calibrate raw attention weights and effectively capture interaction signals between heterophilic node pairs in hypergraphs, we utilize the heterophily discrepancy to adjust information propagation. Taking the service item hypergraph as an example, after computing the initial attention coefficient $e_{u v}$ between node $u$ and node $v$ , we further quantify their feature differences to adjust attention allocation:

\begin{aligned} e_{u v} = LeakyReLU ((h_{u} ⊙ h_{v}) {(a^{ε_{u}^{(H_{v})}})}^{T}) \end{aligned}

(5)

where the attention coefficient

e_{u v} \in R^{d^{'}} \times R^{d^{'}} \to R

denotes the importance of node

v

to node

u

within the hyperedge

ε_{u}^{(H_{v})}

(centered on user

u

). In our experiments, a single-layer feedforward neural network with weight vector

a^{ε_{u}^{(H_{v})}} \in R^{d^{'}}

and LeakyReLU activation is adopted.

To explicitly model the degree of heterophily between nodes, we introduce the discrepancy $m_{u v}$ , which quantifies feature differences via a complementary form of cosine similarity:

\begin{aligned} m_{u v} = 1 - \cos (h_{u}, h_{v}) = 1 - \frac{h_{u} \cdot h_{v}}{‖ h_{u} ‖ \cdot ‖ h_{v} ‖} \end{aligned}

(6)

where

\cos (h_{u}, h_{v})

measures feature similarity between nodes

u

and

v

, while

m_{u v}

focuses on dynamic pairwise differences to adaptively adjust attention weights—higher

m_{u v}

indicates stronger local heterophily, enabling fine-grained modulation of information propagation in hyperedges.

This heterophily discrepancy $m_{u v}$ is leveraged to dynamically calibrate attention weights, enabling the model to allocate higher attention to heterophilic node pairs and thereby effectively mitigate the dominance of homophilic signals in hyperedges:

\begin{aligned} e_{u v}^{'} = e_{u v} \cdot (1 + μ \cdot m_{u v}) \end{aligned}

(7)

To normalize attention coefficients and eliminate magnitude differences, we apply softmax to obtain the final weight coefficient $α_{u v}$ :

\begin{aligned} α_{u v} = softmax (e_{u v}^{'}) = \frac{\exp (e_{u v}^{'})}{\sum_{x \in ε_{u}^{(H_{v})}} \exp (e_{u x}^{'})} \end{aligned}

(8)

The output feature of each node is then obtained by computing the linear combination of features weighted by these coefficients:

\begin{aligned} h_{u}^{'} = \sum_{v \in ε_{u}^{(H_{v})}} α_{u v} \cdot h_{v} \end{aligned}

(9)

Following these steps, we derive the user feature $h_{u}^{'} \in R^{d^{'}}$ in the service item hypergraph. Similarly, service item node representations $h_{v}^{'}$ are obtained by introducing the heterophily metric module to adjust attention weights when aggregating features of interacting users in the user hypergraph, ensuring explicit capture of cross-feature user groups. Through this design, the heterophily-aware attention mechanism explicitly enhances information flow between heterophilic node pairs within hyperedges, enabling generated node representations to more accurately capture heterophily patterns in user-service item interactions and provide differentiated semantic feature inputs for subsequent service recommendation tasks.

5.2. Disentangled hypergraph contrastive module

In the context of hypergraph recommendation, traditional models often overlook the coupling of homophily and heterophily signals, leading to feature confusion and over-smoothing in high-order interaction modeling. The high-order structure of hypergraphs (hyperedges connecting multiple nodes) and the heterophilous feature distribution pose two core challenges for contrastive learning: On one hand, nodes within hyperedges exhibit both homophilous and heterophilous associations, yet traditional models fail to explicitly separate these two types of signals. For example, ‘action games’ and ‘strategy games’ interacted by a user form heterophilous connections in hyperedges but are aggregated as homophilous signals by conventional methods, resulting in blurred feature representations and loss of cross-category interest information. On the other hand, in deep hypergraph convolution, the feature differences of heterophilous nodes are gradually diluted with increasing layers. Especially in strongly heterophilous scenarios where the hypergraph homophily ratio $H (G) < 40 %$ , multi-layer information aggregation causes heterophilous features to collapse into homophilous representations, losing discriminative power.

To address the above challenges, we propose a Disentangled Hypergraph Contrastive Module (DHCM), which explicitly separates homophily and heterophily representations and designs dual contrastive tasks to enhance feature discriminability. The core idea of this module is to decompose high-order interactions within hyperedges into homophilous semantic channels and heterophilous semantic channels. Through contrastive learning, it respectively reinforces the aggregation of homogeneous nodes and the differentiation of heterophilous nodes, thereby breaking through the dependency of traditional models on the “homophily assumption”. Following this line of thought, each graph node is represented as:

\begin{aligned} \begin{aligned} h_{u}^{'} & ≜ h_{u}^{(h o m o)} + h_{u}^{(h e t e r o)}, \\ h_{v}^{'} & ≜ h_{v}^{(h o m o)} + h_{v}^{(h e t e r o)}, \end{aligned} \end{aligned}

(10)

where

h^{(h o m o)} \in R^{d^{'}}

and

h^{(h e t e r o)} \in R^{d^{'}}

denote the homophily and heterophily representations of nodes, respectively. Here

h_{u}^{(h o m o)}

and

h_{u}^{(h e t e r o)}

are learned from two channels of the same attention layer. In the feature space,

h^{(h o m o)}

and

h^{(h e t e r o)}

are statistically independent, each characterizing distinct semantic features of the graph structure;

h^{(h o m o)}

is dedicated to capturing neighborhood homophily and community structures, whereas

h^{(h e t e r o)}

serves to model attribute disparities between nodes.

To enforce the statistical independence between $h^{(h o m o)}$ and $h^{(h e t e r o)}$ , inspired by the heterophily-aware graph representation learning approach of Hetero $^{2}$ Net,¹⁶ we construct a disentangling loss by minimizing the Pearson correlation coefficient:

\begin{aligned} L_{c o r r} = \sum_{n \in V \cup U} \frac{| Cov (h_{n}^{(h o m o)}, h_{n}^{(h e t e r o)}) |}{\sqrt{VAR (h_{n}^{(h o m o)})} \sqrt{VAR (h_{n}^{(h e t e r o)})}} \end{aligned}

(11)

where

Cov (\cdot, \cdot)

and

VAR (\cdot)

denote covariance and variance operations, respectively.

Next, we design a contrastive auxiliary task to learn $h^{(h o m o)}$ and $h^{(h e t e r o)}$ . To enhance the discriminative power of disentangled representations in edge prediction tasks, this auxiliary task introduces a mask-based contrastive mechanism, which acts on hyperedges associated with the user set $U$ (where $U$ denotes the set of all users). Specifically, for each user $u \in U$ , we focus on the hyperedge $ε_{u}^{(H_{v})}$ in the service item hypergraph $H_{v}$ that consists of service items interacted with by user $u$ , and perform random masking operations on some edges within this hyperedge.

Concretely, we randomly select some edges from all possible edges within $ε_{u}^{(H_{v})}$ as ‘masked edges’, while the remaining unmasked edges serve as ‘visible edges’. The reconstruction task aims to predict masked edges based on the features of nodes connected by visible edges. Drawing on the intuition that node pairs within the same hyperedge are more likely to exhibit homophilic relations, while pairs not co-occurring in any hyperedge are more likely to exhibit heterophilic relations, we design our model to maximize their relative similarity under the corresponding representations. In particular:

Homophily contrastive subtask: Encourage node pairs that belong to the same hyperedge to have higher similarity in the $h^{(h o m o)}$ space than pairs that do not, thereby reinforcing homophily signals.

Heterophily contrastive subtask: Enforces that pairs of nodes not belonging to the same hyperedge are more similar in the $h^{(h e t e r o)}$ representation space than pairs that do belong to the same hyperedge.

Accordingly, the contrastive loss is defined as equation (12). This mask-contrastive strategy takes the user set $U$ as its starting point: each user $u \in U$ defines a distinct collection of hyperedges $ε_{u}^{(H_{v})}$ . Within each hyperedge, we randomly mask a small fraction of the truly co-occurring node pairs; these masked pairs become positive samples, while pairs that never co-occur form negative samples. $h^{(h o m o)}$ is then trained to pull the postives closer together than the negatives.

\begin{aligned} L_{u}^{c o n} = L_{u}^{+} + L_{u}^{-} . \end{aligned}

(13)

For pairs $(v_{i}, v_{j}) \in E_{u}$ , where $v_{i}$ and $v_{j}$ are nodes embedded in the hyperedge containing node $u$ , they are designated as positive sample pairs. Conversely, $(v_{m}, v_{n}) \notin E_{u}$ signifies that $v_{m}$ and $v_{n}$ lie outside the hyperedge of node $u$ , serving as negative sample pairs for optimization. The function $θ (\cdot)$ is a standard 2-layer MLP, while $τ$ denotes the temperature parameter, which modulates the smoothness of the similarity distribution.

Similarly, by applying the same approach to the user hypergraph, we obtain $L_{con}^{v}$ . Therefore, the total contrastive loss is:

\begin{aligned} L_{con} = λ_{1} L_{u}^{c o n} + λ_{2} L_{v}^{c o n}, \end{aligned}

(14)

5.3. Dynamic multi-interest learning

Users often exhibit diverse preferences through interactions with multiple heterophilic service items in hypergraphs (e.g., users favoring both action and strategy games in Figure 1), where traditional single user representations struggle to capture such diverse interests. To address this, we design a multi-interest learning module that decouples users’ latent interest spaces to generate dynamic interest representations relevant to target service items, enabling precise modeling of multivariate preferences in heterophilous scenarios.

For user node $u$ , we first generate $K$ interest embeddings through an interest disentangling layer, where each embedding corresponds to an independent latent interest:

\begin{aligned} e_{u i} = softmax (W_{i} h_{u}^{'}) \cdot h_{u}^{'}, i = 1, 2, \dots, K \end{aligned}

(15)

where

W_{i} \in R^{d^{'} \times d^{'}}

is a learnable mapping matrix for the

i

-th interest, projecting the user representation into a specific interest space by weighting different feature dimensions. The softmax function ensures interest weights are normalized, making

e_{u i}

focus on the user’s dominant features in the

i

-th interest dimension. This process explicitly separates the user’s diverse interests, avoiding the blurring of cross-category preferences in a single representation (e.g., mixing action and strategy interests into a vague game preference).

To solve the interest adaptation problem in service recommendations, we introduce a target-oriented attention mechanism to dynamically activate the most relevant interest embeddings based on the features of target service item $v$ :

\begin{aligned} γ_{i} = \frac{\exp (e_{u i}^{T} W_{γ} h_{v}^{'})}{\sum_{j = 1}^{K} \exp (e_{u j}^{T} W_{γ} h_{v}^{'})} \end{aligned}

(16)

where

W_{γ} \in R^{d^{'} \times d^{'}}

is a learnable matrix that maps user interest embeddings and service item representations

h_{v}^{'}

into the same semantic space.

γ_{i}

denotes the activation strength of target service item

v

for the user’s

i

-th interest.

A user representation $s_{u}$ highly relevant to the target service item is then generated via weighted summation:

\begin{aligned} s_{u} = \sum_{i = 1}^{K} γ_{i} e_{u i} \end{aligned}

(17)

5.4. Prediction layer

For user $u$ and service item $v$ , leveraging the user’s dynamic interest representation $s_{u}$ and service item representation $h_{v_{i}}^{'}$ generated by dynamic multi-interest learning, we first use dot product and then apply softmax function to obtain the output $\hat{y}$ :

\begin{aligned} {\hat{y}}_{i} = softmax (s_{u}^{T} h_{v_{i}}^{'}) \end{aligned}

(18)

Where

{\hat{y}}_{i} \in \hat{y}

denotes the probability of service item

v_{i}

appearing as the next-click in the current user. The loss function is defined as the cross-entropy of the prediction result

\hat{y}

\begin{aligned} L_{c e} = - \sum_{i = 1}^{n} y_{i} \log {\hat{y}}_{i} + (1 - y_{i}) \log (1 - {\hat{y}}_{i}) \end{aligned}

(19)

where

y

denotes the one-hot encoding vector of the ground truth service item.

Integrating the disentangling loss in equation (11) , the contrastive loss in equation (14),with the cross-entropy loss equation (19), the overall objective function of $H^{2} O$ GNN is formulated as:

\begin{aligned} L = L_{c e} + L_{c o n} + β L_{c o r r} \end{aligned}

(20)

5.5. Complexity analysis

The space complexity of the model is dominated by three components: hypergraph structure storage, node feature storage, and dynamic multi-interest vector storage. The model exhibits an overall lightweight nature with no redundant space overhead, and the space requirements of each module are as follows: In the hypergraph construction phase, it is necessary to store hyperedge structures ( $O (| E | \cdot k)$ ), where each hyperedge records indices of $k$ nodes, eliminating the need to store the full-graph adjacency matrix; Node feature storage focuses on projected homophily/heterophily disentangled representations ( $O (N \cdot d^{'})$ ), which alleviates space pressure caused by high-dimensional features; The dynamic multi-interest learning module only needs to store $K$ interest vectors of users ( $O (U \cdot K \cdot d^{'})$ ), while service nodes do not require additional interest storage, further reducing space costs. The overall space complexity is $O (N \cdot d^{'} + | E | \cdot k + U \cdot K \cdot d^{'})$ , which features extremely low memory usage. It is compatible with consumer-grade hardware, and no additional high-memory devices are required for deployment.

The time complexity of the model shows linear growth in both training and inference phases, without the full-graph pairwise computation redundancy of traditional GNNs. The time cost consists of four core modules: Hypergraph construction ( $O (N \cdot k)$ ), where $k$ is the average number of nodes per hyperedge and is much smaller than $N$ ; Heterophily-aware attention mechanism ( $O (| E | \cdot k \cdot d^{'})$ ), where attention weights are only computed within hyperedges without full-graph interactions; Hypergraph Disentangled Contrastive Module (DHCM) ( $O (| E | \cdot k^{2} + N \cdot d^{'})$ ), where the contrastive loss only processes sample pairs inside and outside hyperedges; Dynamic multi-interest learning ( $O (U \cdot K \cdot d^{'})$ ), where both interest generation and activation are linear operations. The overall training time complexity is $O (N \cdot d \cdot d^{'} + | E | \cdot k \cdot d^{'} + U \cdot K \cdot d^{'})$ (where $d$ is the input feature dimension), and the dominant terms grow linearly with $N$ and $| E |$ .

In conclusion, while our model incorporates hypergraph construction and dynamic multi-interest learning modules, its overall space complexity remains lightweight (compatible with consumer-grade hardware) and time complexity shows linear growth (without full-graph pairwise redundancy of traditional GNNs), leading to controllable resource consumption. It offers a more effective methodology for service recommendation by accurately capturing both homophily/heterophily signals and high-order interaction semantics in hypergraphs.

6. Experiments

6.1. Datasets

Steam. The raw data was crawled by Mark et al.,⁴⁵ who scraped the ID space from February 28, 2013, to March 18, 2013, discovering a total of 108.7 million user accounts by the end of the crawl. The dataset includes friend lists, owned games, and playtime statistics.

MovieLens. This is a dataset containing movie ratings and user demographic information. Specifically, our experiments use the ML-1M version, which includes 1 million movie ratings from April 2000 to February 2003.

Yelp. This is a large-scale dataset comprising user ratings for businesses. We systematically collect all interactions over the period of January to December 2018 for our experiments.

The statistics of the two datasets after preprocessing are detailed in Table 2.

Table 2.
Description of datasets.

Statistics Steam MovieLens Yelp

Users 6037 5875 25802

Service Items 2170 3925 17445

Interactions 119385 560610 284401

Avg.Lens 19.78 95.45 26.98

Density $1.76 \times 10^{- 3}$ $6.97 \times 10^{- 3}$ $6.31 \times 10^{- 3}$

homophily 48.13% 62.93% 73.97%

Statistics	Steam	MovieLens	Yelp
Users	6037	5875	25802
Service Items	2170	3925	17445
Interactions	119385	560610	284401
Avg.Lens	19.78	95.45	26.98
Density	$1.76 \times 10^{- 3}$	$6.97 \times 10^{- 3}$	$6.31 \times 10^{- 3}$
homophily	48.13%	62.93%	73.97%

6.2. Evaluation metrics

We selected two widely used metrics in service recommendation tasks, Recall@K and Normalized Discounted Cumulative Gain@K (NDCG@K),^46,47 to evaluate the performance of our model and baselines. Here, $K$ is set to 5, 10, and 20. In each dataset, we randomly split the data into 60%, 20%, and 20% as the training set, test set, and validation set, respectively.

6.3. Baselines

We compared our model with several state-of-the-art methods:

GCN⁴³: A fundamental graph neural network model that aggregates node neighbor information through graph convolution operations to learn node representations in graph structures.

LightGCN⁷: This is a streamlined version of GCN, omitting the feature transformations and non-linear activations present in traditional GCN.

GCE-GNN⁴⁸: A session-based recommendation (without explicit user identities, relying on interaction sequences within sessions) GNN model. It captures users’ short-term interaction behaviors through graph neural networks enhanced by global context.

DHCF¹²: A hypergraph-aware divide-and-conquer recommendation approach using a two-channel hypergraph neural network to achieve separate and simultaneous learning of user and service item embeddings.

SHT¹³: A hypergraph-aware transformer based approach employing hypergraph attention strategies. The model further proposes a data augmentation method by supplementing CF signals with different perspectives.

HMGSR⁴⁹: This presents a hierarchical attention mechanism to learn higher-order features on motif adjacency matrices.

Hetero $^{2}$ Net¹⁶: A heterophily-aware heterogeneous graph representation learning method focused on handling semantic correlations among multiple node and edge types in heterogeneous graphs.

DMI-GNN²⁶: A multi-inteCaptures users’ dynamic multi-interest preferences in sessions, modeling the diversity and evolution of interests via graph neural networks.

6.4. Parameter settings

We conducted experiments on an Ubuntu server equipped with an Intel Xeon Silver 4210 CPU, an NVIDIA A100 SXM4 GPU (40GB), and 251GB of RAM. The model was implemented in PyTorch 2.0 and compiled in a Python 3.10 environment.

To achieve optimal performance, we fine-tuned all hyperparameters and report the key settings. The experiments were trained using the AdamW optimizer with mini-batch gradient descent. Through empirical optimization, we determine the hyper-parameters of our model as follows:

The initial learning rate ( $η$ ) is set to ${0.001, 0.002, 0.005}$ and the dropout is set to ${0.6, 0.3, 0.5}$ .

Batch Size is set to ${512, 512, 512}$ .

Contrastive Loss Weight ( $λ_{1}$ ) is set to ${0.4, 0.5, 0.4}$ and the contrastive Loss Weight ( $λ_{2}$ ) is set to ${0.3, 0.2, 0.1}$ .

Number of Interests ( $K$ ) is set to ${3, 5, 3}$ and the temperature ( $τ$ ) is set to ${0.3, 0.5, 0.7}$ .

Disentangling Loss ( $β$ ) is set to ${0.1, 0.2, 0.3}$ .

The number of hidden dimensions in one head of multi-level attention mechanism $F^{r} = 32$ .

The number of multi-head attention mechanism $G = 12$ .

Epochs (with Early Stopping) are set to 100-200 (Patience=10).

For all baselines, we utilized the source code provided by the authors and performed hyperparameter tuning. We then compared these optimized results with those of our proposed model.

6.5. Performance comparison

Tables 3 and 4 ,5 summarize the experimental results of all models on the three datasets. The optimal performance for each evaluation metric is highlighted in bold. Experimental results demonstrate that our model exhibits significant advantages in both strong heterophily (Steam) and moderate heterophily (MovieLens) scenarios, with its core strengths stemming from the precise modeling of high-order heterophilic interactions and users’ diverse preferences.

Table 3.
Performance comparison of $H^{2} O$ GNN and baseline models on the steam dataset.

Steam

Model Recall@5 NDCG@5 Recall@10 NDCG@10 Recall@20 NDCG@20

GCE-GNN 0.1212 0.0804 0.1846 0.1008 0.2530 0.1180

DMI-GNN 0.1299 0.0921 0.1918 0.1101 0.2665 0.1284

DHCF 0.1376 0.1128 0.2375 0.1478 0.3190 0.1739

GCN 0.1800 0.0970 0.2401 0.1157 0.3206 0.1356

LightGCN 0.2015 0.1123 0.2789 0.1402 0.3652 0.1689

SHT 0.2580 0.1702 0.3485 0.2188 0.4640 0.2484

HMGSR 0.2734 0.1784 0.3644 0.2204 0.4953 0.2498

Hetero $^{2}$ Net 0.2150 0.1421 0.2875 0.1655 0.3700 0.1865

Ours 0.3000 0.1841 0.4400 0.2258 0.5650 0.2539

	Steam
GCE-GNN	0.1212	0.0804	0.1846	0.1008	0.2530	0.1180
DMI-GNN	0.1299	0.0921	0.1918	0.1101	0.2665	0.1284
DHCF	0.1376	0.1128	0.2375	0.1478	0.3190	0.1739
GCN	0.1800	0.0970	0.2401	0.1157	0.3206	0.1356
LightGCN	0.2015	0.1123	0.2789	0.1402	0.3652	0.1689
SHT	0.2580	0.1702	0.3485	0.2188	0.4640	0.2484
HMGSR	0.2734	0.1784	0.3644	0.2204	0.4953	0.2498
Hetero $^{2}$ Net	0.2150	0.1421	0.2875	0.1655	0.3700	0.1865
Ours	0.3000	0.1841	0.4400	0.2258	0.5650	0.2539

Table 4.

Performance comparison of $H^{2} O$ GNN and baseline models on the movieLens dataset.

	MovieLens
Model	Recall@5	NDCG@5	Recall@10	NDCG@10	Recall@20	NDCG@20
GCE-GNN	0.1484	0.1087	0.2061	0.1272	0.2674	0.1427
DMI-GNN	0.2601	0.1588	0.4000	0.2040	0.5440	0.2405
DHCF	0.3472	0.2598	0.4836	0.2973	0.5724	0.3288
GCN	0.3667	0.2675	0.5083	0.3156	0.5833	0.3345
LightGCN	0.3945	0.2784	0.5287	0.3287	0.6014	0.3485
SHT	0.3833	0.2608	0.5158	0.3033	0.6067	0.3335
HMGSR	0.3844	0.2683	0.5209	0.3144	0.6178	0.3398
Hetero $^{2}$ Net	0.2458	0.1677	0.3292	0.1946	0.4625	0.2283
Ours	0.4375	0.2849	0.5458	0.3206	0.6917	0.3567

Table 5.

Performance comparison of $H^{2} O$ GNN and baseline models on the yelp dataset.

	Yelp
Model	Recall@5	NDCG@5	Recall@10	NDCG@10	Recall@20	NDCG@20
GCE-GNN	0.1484	0.1087	0.2061	0.1272	0.2674	0.1427
DMI-GNN	0.2601	0.1588	0.4000	0.2040	0.5440	0.2405
DHCF	0.3472	0.2598	0.4836	0.2973	0.5724	0.3288
GCN	0.3667	0.2675	0.5083	0.3156	0.5833	0.3345
LightGCN	0.3752	0.2854	0.5377	0.3301	0.6012	0.3424
SHT	0.3833	0.2608	0.5158	0.3033	0.6067	0.3335
HMGSR	0.3879	0.2642	0.5387	0.3155	0.6208	0.3459
Hetero $^{2}$ Net	0.2458	0.1677	0.3292	0.1946	0.4625	0.2283
Ours	0.5025	0.3507	0.6189	0.3744	0.7073	0.4651

When comparing different types of baseline models, traditional GNNs and session-based models reveal significant limitations. As a fundamental graph convolutional model, GCN achieves an NDCG@20 of only 13.56% on the Steam dataset, less than half of our model’s performance. This stems from its reliance on binary edge modeling, which fails to capture multi-node interactions within hyperedges (e.g., users interacting with multiple heterophilic service items simultaneously), and the lack of heterophily awareness leads to the loss of cross-category interest information. Session-based models GCE-GNN and DMI-GNN, focusing on short-term interaction sequences or lacking explicit user identities, perform poorly in long-term preference modeling. For example, DMI-GNN achieves a Recall@20 of only 26.65% on Steam, far lower than our model’s 56.25%.

Although hypergraph-based baseline models SHT and DHCF can model high-order interactions, their performance is limited by the lack of explicit heterophily handling. SHT integrates global signals through hypergraph transformation and attention mechanisms, achieving an NDCG@10 of 21.88% on Steam. However, due to the failure to calibrate weights for heterophilic nodes, the dominance of homophily signals undervalues the information contribution of cross-feature users (e.g., different age groups). DHCF uses a two-pass hypergraph neural network to separate user/service item embeddings, achieving a Recall@20 of 57.24% on MovieLens. However, the absence of a heterophily-aware mechanism prevents it from effectively distinguishing the semantic features of heterophilic service items within hyperedges (e.g., movie genre differences), resulting in a recommendation accuracy 12.9% lower than our model.

The heterophilic graph model Hetero $^{2}$ Net focuses on node-type differences but does not adapt to the high-order structure of hypergraphs (e.g., user-centered star hyperedges) and lacks a hypergraph-specific homophily metric. It achieves a Recall@20 of only 46.25% on MovieLens, significantly lower than our model’s 69.17%. This indicates that the meta-path mechanisms relied upon by heterophilic graph methods are difficult to transfer to multi-node association scenarios in hypergraphs. In contrast, our model explicitly constructs high-order interactions through star hyperedges and dynamically adjusts attention weights using heterophily metrics, effectively addressing this issue.

6.6. Ablation study

To evaluate the contributions of key components to the overall performance of the model, we conducted ablation experiments on the Steam and MovieLens datasets. As shown in Table 6, we evaluated different model variants: (1) ‘w/o 1’: Uses only the standard GAT module without the heterophily-aware mechanism. (2) ‘w/o 2’: Excludes the contrastive learning module. (3) ‘w/o 3’: Omits the multi-interest learning component, directly computing the dot product between user and service item representations from the previous step.

Table 6.
Performance comparison of ablation study.

Model Steam MovieLens Yelp

Recall@20 NDCG@20 Recall@20 NDCG@20 Recall@20 NDCG@20

whole 0.5650 0.2539 0.6917 0.3567 0.7073 0.4651

w/o 1 0.5000 0.2195 0.6433 0.3224 0.6579 0.4432

w/o 2 0.4900 0.2147 0.6379 0.3154 0.6634 0.4577

w/o 3 0.4625 0.2194 0.6009 0.3057 0.6153 0.4257

Model	Steam	MovieLens	Yelp
whole	0.5650	0.2539	0.6917	0.3567	0.7073	0.4651
w/o 1	0.5000	0.2195	0.6433	0.3224	0.6579	0.4432
w/o 2	0.4900	0.2147	0.6379	0.3154	0.6634	0.4577
w/o 3	0.4625	0.2194	0.6009	0.3057	0.6153	0.4257

From the results, we observe significant performance degradation across core metrics on both datasets when removing the heterophily-aware mechanism (variant ‘w/o 1’). This indicates that the mechanism effectively captures complex interaction patterns in heterophilic graphs, enhancing feature aggregation efficiency between different node types and significantly improving the model’s ability to capture user preferences. Without this mechanism, the graph attention module defaults to conventional homophily-based aggregation, failing to leverage complementary information in heterophilic structures and thus reducing recommendation accuracy.Removing the contrastive module (variant ‘w/o 2’) leads to a further decline in performance. The auxiliary module provides regularization constraints through additional supervision signals (e.g., temporal features of user behavior or service item context attributes), mitigating overfitting. Its absence weakens the model’s generalization ability, particularly in sparse interaction scenarios, where it cannot infer latent user interests from multi-dimensional information, thereby affecting recommendation diversity and accuracy. Eliminating the multi-interest learning module (variant ‘w/o 3’) results in the most substantial performance drop, underscoring its critical role in capturing dynamic and diverse user preferences. By disentangling user representations into multiple interest vectors, the module enables finer-grained matching with multi-dimensional service item features, avoiding the oversimplification of user interests inherent in direct dot-product operations. Without this component, the model fails to adapt to users’ contextual needs, especially in long-term interaction scenarios, leading to a significant decline in recommendation quality.

The ablation results systematically validate the indispensability of each core component: the heterophily-aware mechanism enhances structural modeling through optimized information aggregation in heterophilic graphs, the contrastive module strengthens generalization via multi-source supervision, and multi-interest learning enables precise preference matching through disentangled user representations. These components form a synergistic framework that collectively enables high-precision recommendation. The data further demonstrate that in complex recommendation scenarios, models relying solely on basic interaction modeling or simplistic feature matching struggle to address the diversity and dynamics of user interests, necessitating structured designs and multi-dimensional feature fusion for performance breakthroughs.

6.7. Cold-Start evaluation

Cold-start is a prevalent challenge in practical service recommendation, primarily manifesting as user cold-start (new users with $< 5$ interactions) and service cold-start (new service items with $< 10$ interactions). The core pain point lies in insufficient interaction data, which makes it difficult for traditional models to capture latent preferences (for new users) or semantic correlations (for new services). This section analyzes the adaptability of $H^{2} O$ GNN to cold-start scenarios and verifies its effectiveness through subset experiments(taking the Yelp dataset as an example).

As shown in Table 7, $H^{2} O$ GNN outperforms all baselines on both subsets: in user cold-start, its Recall@20 is higher than SHT and DHCF; in service cold-start, its Recall@20 is higher than SHT and DHCF. This confirms that $H^{2} O$ GNN effectively alleviates the sparsity problem in cold-start scenarios through hypergraph-based high-order interaction modeling and heterophily-aware mechanisms.

Table 7.
Cold-start evaluation.

Scenario Model Recall@10 NDCG@10 Recall@20 NDCG@20

User Cold-Start SHT 0.2843 0.1899 0.3284 0.2073

DHCF 0.2971 0.1984 0.3453 0.2192

Hetero $^{2}$ Net 0.2612 0.1722 0.3024 0.1914

$H^{2} O$ GNN 0.3565 0.2346 0.4125 0.2584

Service Cold-Start SHT 0.3014 0.2033 0.3475 0.2251

DHCF 0.3159 0.2158 0.3684 0.2388

Hetero $^{2}$ Net 0.2734 0.1855 0.3195 0.2044

$H^{2} O$ GNN 0.3822 0.2414 0.4354 0.2697

Scenario	Model	Recall@10	NDCG@10	Recall@20	NDCG@20
User Cold-Start	SHT	0.2843	0.1899	0.3284	0.2073
	DHCF	0.2971	0.1984	0.3453	0.2192
	Hetero $^{2}$ Net	0.2612	0.1722	0.3024	0.1914
	$H^{2} O$ GNN	0.3565	0.2346	0.4125	0.2584
Service Cold-Start	SHT	0.3014	0.2033	0.3475	0.2251
	DHCF	0.3159	0.2158	0.3684	0.2388
	Hetero $^{2}$ Net	0.2734	0.1855	0.3195	0.2044
	$H^{2} O$ GNN	0.3822	0.2414	0.4354	0.2697

6.8. Sensitivity of parameters

We also investigated the impact of the number of interests on model performance. As illustrated in Figure 3, on the Steam dataset, as the number of interests increases, the Recall@20 and NDCG@20 metrics exhibit a trend of first increasing and then decreasing. When the number of interests is 3, both metrics reach their peaks, at which point the model most efficiently captures and utilizes users’ diverse interests. A similar trend is observed on the MovieLens dataset, where Recall@20 and NDCG@20 achieve their highest values when the number of interests is 5. These results indicate that for different datasets, an optimal number of interests exists, which can effectively disentangle users’ diverse preferences while avoiding information redundancy or deficiency caused by excessive or insufficient interest dimensions. This validates the critical role of reasonably setting the number of interests in the dynamic multi-interest learning module for achieving precise matching of user needs in recommendations.

Figure 3.

The impact of interests number $K$ .

Figure 4 explores the influence of the parameter $τ$ in equation (12) on the model performance. As a temperature parameter in the contrastive loss function, $τ$ dynamically balances the semantic learning of homophily and heterophily signals by regulating the temperature of the softmax distribution. In Figure 4, on the Steam dataset (with strong heterophily), $τ$ = 0.3 yields the peak values for Recall@20 and NDCG@20, indicating that a lower temperature enhances the model’s sensitivity to subtle feature differences among heterophilic nodes, thus strengthening the disentangling of heterophily signals. Conversely, on the MovieLens dataset (with moderate heterophily), the optimal performance is achieved at $τ$ = 0.5, suggesting that a moderately higher temperature is required in moderate heterophily scenarios to integrate global similarities (e.g., homophily semantics among users with similar movie preferences).Experimental results reveal a negative correlation between the optimal $τ$ value and the degree of heterophily in datasets: the stronger the heterophily, the lower the optimal $τ$ , verifying its adaptability to data characteristics. Excessively high $τ$ causes the similarity distribution to become overly smooth, leading to confusion between homophily and heterophily signals and degrading feature discrimination. Conversely, excessively low $τ$ induces overfitting due to excessive focus on local differences, both reducing recommendation performance.In summary, $τ$ directly influences the modeling of high-order interactions by the Hypergraph Disentangling Contrastive Module through controlling the signal separation precision in contrastive loss. Its dynamic adjustment mechanism is crucial for adapting to different heterophily scenarios and optimizing recommendation performance, providing empirical evidence for parameter optimization in feature disentangled and contrastive learning within heterophily-aware recommendation systems.

Figure 4.

The impact of the hyperparameter $τ$ .

6.9. Visual analysis of the impact of node disentanglement

To intuitively verify the ability of the DHCM module to decouple homophily-heterophily signals of nodes, we conduct a visualization analysis of node embeddings at different training stages. By observing the distribution of nodes and their connection relationships in a 2D space, we quantify the decoupling effect of the module.

Multiple types of nodes are selected for the experiment. Node embeddings are extracted at four key training stages: the 1st epoch, 40th epoch, 80th epoch, and 120th epoch. Their distribution characteristics are visualized via 2D dimensionality reduction ( $t - SNE$ ). In these figures, each data point represents the result of dimensionality reduction applied to the node embeddings. Each high-dimensional embedding is transformed into a two-dimensional vector $[t - SNE 1, t - SNE 2]$ , where the horizontal axis denotes the first-dimensional feature $t - SNE 1$ of the node embedding after dimensionality reduction, and the vertical axis denotes the second-dimensional feature $t - SNE 2$ . A light gray line is used to mark the “homophily–heterophily decoupling” relationship between each pair of nodes, intuitively demonstrating the separation process of homophily and heterophily signals of the same node under the action of the DHCM module. From the 1st epoch (Figure5(a)) to convergence at the 120th epoch (Figure 5(d)), node embeddings and DHCM’s decoupling effect evolve progressively: initially, embeddings are concentrated, homophily/heterophily signals are undistinguished, and the module is inactive; at the 40th epoch, nodes start separating along $d_{1} = 0$ , lines disperse, and preliminary decoupling is achieved; by the 80th epoch, separation intensifies with a distinct “dual-cluster” structure and stronger decoupling; finally, optimal separation is reached, signals are fully differentiated, and the module realizes complete node signal decoupling.

Figure 5.

Impact of node disentanglement.

The core function of the DHCM module is to explicitly separate the “homophily signals” and “heterophily signals” in node representations: From a process perspective, it promotes node embeddings to evolve gradually from “mixed representations” to “dual-cluster separated representations”, with the decoupling degree improving monotonically with the number of training epochs; From an effect perspective, complete decoupling lays the foundation for subsequent “homophily aggregation” and “heterophily interaction”, enabling the model to more accurately capture the two types of core relationships in the user-service network and ultimately improve recommendation performance. Through the above visualization analysis, the decoupling ability of the DHCM module is intuitively verified, providing visual-level support for its effectiveness in user-service recommendation tasks.

7. Conclusion

Against the backdrop of challenges in modeling users’ diverse preferences and strongly heterophilous interactions in digital service recommendation, this paper proposes the $H^{2} O$ GNN model. Through the Hypergraph Disentangling Contrastive Module, it explicitly separates homophily and heterophily signals, dynamically enhances information propagation between heterophilic nodes using a heterophily-aware attention mechanism, and precisely captures users’ cross-category preferences via dynamic multi-interest learning. This represents the first systematic integration of heterophily awareness into high-order interaction modeling. Experimental results on two datasets demonstrate the significant superiority of $H^{2} O$ GNN over other representative baselines, particularly in low-homophily scenarios. Ablation studies validate the necessity of each module. While the model still has room for improvement in multimodal data processing (e.g., fusing text like service descriptions via BERT or visuals like posters via CNN into node features, integrating temporal interaction windows into hypergraphs), hypergraph scalability, and cold-start scenarios, it establishes a novel paradigm for heterophily-aware recommendation. The proposed methodologies can be extended to broader heterophilic graph learning tasks, offering both theoretical contributions and practical value for precise recommendation in complex interaction scenarios.

Footnotes

Acknowledgements

This work is supported by the Joint Fund Key Program of the National Natural Science Foundation of China(U23B2029) and Projects of International Cooperation and Exchanges NSFC (Grant No. 62061136006).

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ORCID iDs

Hongying Qian

Guiling Wang

Hongkai Wu

Jianye Yang

Yu Gao

Jing Gao

Jian Yu

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		Overall GCN	Overall GCN
Dataset	$H (G)$ (%)	Recall@20	NDCG@20
Steam	37.45	0.3158	0.1246
	48.13	0.3284	0.1356
	71.36	0.5942	0.3141
	87.73	0.6433	0.3245
MovieLens	42.19	0.4001	0.2844
	55.54	0.4100	0.2889
	62.93	0.5833	0.3345
	74.85	0.6045	0.3469

H 2 O GNN: Hypergraph-based heterophily-aware neural network for service recommendation

Abstract

Keywords

1. Introduction

2.1. Traditional collaborative filtering and graph neural network-based service recommendation

2.2. Hypergraph neural networks and high-Order interaction modeling

2.3. Heterophily learning

2.4. Multi-Interest modeling, dynamic preference disentangling and others

3. Problem formulation

3.1. Service interaction graph

3.2. User-Service item hypergraphs

3.3. Heterophily in hypergraphs

3.4. Hypergraph homophily ratio

4. Empirical observations

6. Experiments

6.1. Datasets

Table 2. Description of datasets. Statistics Steam MovieLens Yelp Users 6037 5875 25802 Service Items 2170 3925 17445 Interactions 119385 560610 284401 Avg.Lens 19.78 95.45 26.98 Density 1.76 × 10 − 3 6.97 × 10 − 3 6.31 × 10 − 3 homophily 48.13% 62.93% 73.97%

6.3. Baselines

6.4. Parameter settings

6.5. Performance comparison

Footnotes

Acknowledgements

Funding

Declaration of conflicting interests

ORCID iDs

References

Table 2.
Description of datasets.

Statistics Steam MovieLens Yelp

Users 6037 5875 25802

Service Items 2170 3925 17445

Interactions 119385 560610 284401

Avg.Lens 19.78 95.45 26.98

Density $1.76 \times 10^{- 3}$ $6.97 \times 10^{- 3}$ $6.31 \times 10^{- 3}$

homophily 48.13% 62.93% 73.97%