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Self-Supervised Multi-Channel Hypergraph Convolutional Network for Social Recommendation
Junliang Yu, Hongzhi Yin, Jundong Li, Qinyong Wang, Nguyen Quoc Viet Hung, Xiangliang Zhang
TL;DR
Social recommendation seeks to improve sparse user-item recommendation, but pairwise models underrepresent high-order user relations. The paper proposes MHCN with motif-induced hypergraph channels and hierarchical self-supervision to preserve connectivity information, reporting superior performance across real-world datasets and gains from the auxiliary task.
Problem
Existing social recommendation models mainly exploit pairwise user relations, while complex high-order relations are under-modeled and hypergraph potential in social recommendation remains under-explored.
Method
MHCN encodes different motif-induced hypergraphs in separate channels and integrates hierarchical mutual-information self-supervision over user, local sub-hypergraph, and global hypergraph representations.
Results
5.389% average improvement in general recommendation and 9.442% in cold-start recommendation are reported for S2-MHCN compared with MHCN.
Takeaways & Limitations
Experiments and ablations support the effectiveness of multi-channel high-order modeling and the self-supervised auxiliary task for social recommendation.
Takeaways & Limitations
The model uniformly assigns every hyperedge weight to one, so its hypergraph weight matrix is the identity matrix.
Abstract
from arXiv · showhide
Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via https://github.com/Coder-Yu/RecQ.
1 INTRODUCTION
Social recommendation uses social relations to address sparse user-item interactions, but conventional GNN-based models mainly capture pairwise connections and miss complex high-order user relations. MHCN models multiple motif-induced hypergraphs, while hierarchical self-supervision helps preserve connectivity information lost during channel aggregation.
- Motivation: Social relations help infer preferences for users with few item interactions, mitigating recommendation data sparsity.The approach relies on friends’ interactions to improve recommendations when a user has limited consumption data.
- Motivation: GNN-based social recommendation models typically represent user-user and user-item interactions as pairwise graphs, overlooking complex high-order relation patterns.Multi-hop propagation can capture long-range dependencies but not the richer patterns beyond pairwise relations.
- Method: MHCN constructs motif-induced hypergraphs so separate channels encode distinct high-order relations, including shared friends and shared purchases.The channels correspond to triangular motifs with underlying semantics.
- Method: Hierarchical mutual-information maximization uses user, user-centered sub-hypergraph, and global-hypergraph representations to recover connectivity information obscured by aggregation.The self-supervised task is designed to preserve local and global high-order connectivity across different hypergraphs.
- Evaluation: Experiments on multiple real-world datasets and ablations report superior performance and validate both the multi-channel architecture and self-supervised task.The contribution claims include extensive evaluation and component-level ablation.
2 RELATED WORK
Related work progresses from matrix-factorization approaches that incorporate social information to GNN models that represent social recommendation with pairwise graphs. Hypergraph and self-supervised learning have been explored separately or in limited recommender-system settings, leaving room for their combination in social recommendation.
- Social Recommendation: Early social recommendation research mainly used matrix factorization through co-factorization, ensemble, and regularization strategies.These methods incorporate social relations as prior knowledge or constraints within flexible MF frameworks.
- Social Recommendation: Deep social recommendation models use GNNs to capture latent preferences, social diffusion, attention-based effects, session interests, and adversarial representations.The cited models generally process user-user and user-item interactions as graph data.
- Hypergraph in Recommender Systems: Hypergraph methods model complex correlations and have been applied to recommendation, but their use in social recommendation remains limited.Prior applications include music recommendation, next-item recommendation, collaborative filtering, and social-network analysis.
- Self-Supervised Learning: Self-supervised learning creates auxiliary supervision from raw data and has extended from image transformations to graph representation learning.Graph methods develop supervision signals by exploiting graph structure or node properties.
- Self-Supervised Learning: Existing recommender-system self-supervision mines sequential context or masks user and item attributes, approaches not readily transferable to social recommendation.The related-work discussion identifies temporal and attribute-based signals as the main existing directions.
3.1 Preliminaries
The preliminaries define users, items, binary user-item interactions, layered user and item embeddings, and hypergraph structure through vertices, hyperedges, weights, and incidence matrices. In this model, hyperedge weights are uniformly set to one.
- Notation: U denotes the user set of size m, I denotes the item set of size n, and R is the binary user-item interaction matrix.r_ui = 1 indicates consumption, while r_ui = 0 indicates that the item is unexposed to the user.
- Notation: P^(l) and Q^(l) denote user and item embeddings of dimension d learned at convolutional layer l.The model uses multiple convolutional layers and records embeddings at each layer.
- Hypergraph Definition: A hypergraph G=(V,E) contains N vertices and M hyperedges, with each hyperedge allowed to contain any number of vertices.The incidence matrix H records whether vertex v_i belongs to hyperedge ε.
- Hypergraph Definition: Hyperedge weights are uniformly assigned one, making the weight matrix W an identity matrix.This is the stated weighting assumption for the paper’s hypergraphs.
3.2 Multi-Channel Hypergraph Convolutional Network for Social Recommendation
MHCN models three types of high-order user relations as separate motif-induced hypergraph channels, convolves each channel, and attentively aggregates their representations for recommendation.
- Hypergraph Construction: MHCN constructs social, joint, and purchase motif-induced hypergraphs to encode distinct high-order user relation patterns.Social motifs capture relations such as mutual friends, joint motifs capture friends purchasing the same item, and purchase motifs capture socially disconnected users sharing purchases.
- Multi-Channel Hypergraph Convolution: The model uses three channels—Social, Joint, and Purchase—with each channel responsible for encoding one high-order relation pattern.The channel count can be adjusted for more sophisticated relational settings.
- Multi-Channel Hypergraph Convolution: Each channel applies hypergraph convolution to propagate user information through motif-induced hyperedges and learn high-order-aware user representations.The model removes learnable linear transformations and nonlinear activations, following LightGCN-style propagation.
- Multi-Channel Hypergraph Convolution: Motif-induced adjacency matrices replace explicit hyperedge computations, enabling efficient sparse matrix calculation for the triangular motifs.The construction exploits sparse matrix multiplications and filters dense purchase-motif entries using popularity and threshold criteria.
- Learning Comprehensive User Representations: Attention selectively aggregates channel-specific user embeddings, while user-item graph convolution adds purchase information absent from the hypergraph channels.The attention mechanism learns per-user contributions from the social, joint, and purchase channels.
- Model Optimization: The recommendation objective trains MHCN with positive purchased items and randomly sampled negative items using a pairwise ranking loss.The predicted score is the inner product between a user representation and an item representation.
3.3 Enhancing MHCN with Self-Supervised Learning
The model adds a self-supervised auxiliary task because channel aggregation can obscure high-order connectivity information. It hierarchically maximizes mutual information across users, local sub-hypergraphs, and whole hypergraphs during joint training.
- Motivation: Channel aggregation may lose inherent characteristics of different high-order connectivity patterns because channels learn embeddings with varying distributions.Concatenation is described as an alternative, but it uniformly weights the contributions of different relation types.
- Self-Supervised Learning: The self-supervised task extends graph-node mutual information maximization to the hierarchical structure of hypergraphs.The design targets finer-grained structural information than coarse graph-node mutual information.
- Hierarchical Mutual Information: For each channel, the hierarchy links a user node, its user-centered sub-hypergraph, and the full hypergraph.Rows of the channel adjacency matrix represent subgraphs centered on the corresponding users.
- Hierarchical Mutual Information: The objective maximizes mutual information between representations of users, centered sub-hypergraphs, and whole hypergraphs to preserve local and global connectivity patterns.The paper frames these structures as informative for inferring user preferences through reductions in structural uncertainty.
- Representation Readout: A gated permutation-invariant readout forms sub-hypergraph representations, while average pooling summarizes them into graph-level representations.The gate controls user-embedding magnitudes, considers adjacency-based user importance, and helps mitigate overfitting and gradient conflict.
- Model Optimization: The auxiliary task uses pairwise ranking to score agreement between positive user-structure pairs and shuffled negative representations, then jointly trains with recommendation.The discriminator is implemented as a dot product, and row-wise and column-wise shuffling corrupts representations to create negatives.
3.4 Complexity Analysis
The model’s complexity is driven by hypergraph and graph convolution, attention, self-gating, and mutual-information maximization, with sparse propagation costs and lower complexity than prior GNN-based social recommendation models.
- Model size: The model’s trainable parameters comprise user and item embeddings, seven gates, and attention parameters.Four gates support MHCN and three support the self-supervised task; each gate and the attention parameters have size (d + 1) × d.
- Time complexity: Through L layers, multi-channel hypergraph convolution costs less than O(|A+|dL), where |A+| is the maximum channel incidence sparsity.The graph convolution additionally costs O(|R+|dL).
- Time complexity: Attention and self-gating each contribute O(md^2), while mutual-information maximization mainly costs O(|A+|d).The analysis omits learnable linear transformations and nonlinear activations, reducing complexity relative to previous GNN-based social recommendation models.
4 EXPERIMENTS AND RESULTS
Experiments on LastFM, Douban, and Yelp evaluate general and cold-start recommendation using ranking metrics, component ablations, and sensitivity analyses. Results support multi-channel hypergraph modeling and hierarchical self-supervision, with performance sensitive to auxiliary-task weight and depth.
- Experimental setup: Experiments use LastFM, Douban, and Yelp with five-fold cross-validation and compare MF-based and GNN-based recommendation baselines.Douban ratings below 4 are removed and the remaining ratings are binarized.
- Experimental setup: Precision@10, Recall@10, and NDCG@10 are computed by ranking all candidate items rather than sampled item sets.Evaluation covers both the complete test set and a cold-start test set containing users with fewer than 20 interactions.
- Recommendation performance: 5.389% improvement in general recommendation and 9.442% in cold-start recommendation are achieved by S2-MHCN over MHCN on average.MHCN without self-supervision already beats all baselines, while self-supervision provides particularly large gains for cold-start recommendation.
- Investigation of Multi-Channel Setting: Removing any channel degrades performance, with the Purchase channel contributing most to the final recommendation results.Social contributes slightly more than Joint on LastFM and Yelp, whereas Joint is more important on Douban.
- Investigation of Multi-Channel Setting: Purchase receives the greatest attention influence for most LastFM users, while Social has limited influence and Joint lies between them.The paper suggests social-only connections may be noisy because socially connected users do not always share preferences.
- Investigation of Self-supervised Task: Hierarchical MIM performs best among self-supervised variants, while local MIM ranks second and DGI can lower performance on some metrics.These comparisons support the proposed hierarchical mutual-information design over the node-graph MIM used in DGI.
- Parameter Sensitivity Analysis: The self-supervised-task weight β peaks at 0.01 across datasets, after which performance steadily declines.The auxiliary task is sensitive to its magnitude: small values help recommendation, whereas larger values can mislead it.
- Parameter Sensitivity Analysis: Two layers yield the best S2-MHCN performance, while deeper models decline across all datasets.The authors associate this decline with over-smoothing from aggregating increasingly distant high-order information.
5 CONCLUSION
MHCN addresses the under-explored use of high-order user relations in social recommendation by combining multi-channel hypergraph modeling with hierarchical mutual-information self-supervision. Experiments on three public datasets verify its components and state-of-the-art performance.
- MHCN models multiple motif-induced hypergraphs to capture high-order user relations in social recommendation.
- Hierarchical mutual information between user, user-centered sub-hypergraph, and hypergraph representations compensates for aggregation loss.
- Experiments on three public datasets verify MHCN’s components and demonstrate state-of-the-art performance.