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Multi-Graph Convolution Collaborative Filtering

Jianing Sun, Yingxue Zhang, Chen Ma, Mark Coates, Huifeng Guo, Ruiming Tang, Xiuqiang He

arXiv:2001.00267v1cs.IR

TL;DR

Existing recommendation methods do not fully exploit user-item interactions and user-user or item-item similarities when learning embeddings. Multi-GCCF addresses this gap with graph convolution over multiple graphs and type-specific processing, and experiments on four benchmarks show significant improvements while ablations verify each component's effectiveness.

  • Problem

    Existing recommendation methods do not fully use user-item interactions and user-user or item-item similarities in embedding learning.

  • Method

    Multi-GCCF jointly processes user-item, user-user, and item-item graphs, using separate graph-convolution functions for users and items.

  • Results

    Experiments on four real-world datasets show Multi-GCCF's superiority over state-of-the-art collaborative filtering and graph neural recommendation models.

  • Takeaways & Limitations

    Ablation studies show that the Bipar-GCN layer, multi-graph encoding layer, and skip connection each contribute to performance, with their combination improving further.

Abstract

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Personalized recommendation is ubiquitous, playing an important role in many online services. Substantial research has been dedicated to learning vector representations of users and items with the goal of predicting a user's preference for an item based on the similarity of the representations. Techniques range from classic matrix factorization to more recent deep learning based methods. However, we argue that existing methods do not make full use of the information that is available from user-item interaction data and the similarities between user pairs and item pairs. In this work, we develop a graph convolution-based recommendation framework, named Multi-Graph Convolution Collaborative Filtering (Multi-GCCF), which explicitly incorporates multiple graphs in the embedding learning process. Multi-GCCF not only expressively models the high-order information via a partite user-item interaction graph, but also integrates the proximal information by building and processing user-user and item-item graphs. Furthermore, we consider the intrinsic difference between user nodes and item nodes when performing graph convolution on the bipartite graph. We conduct extensive experiments on four publicly accessible benchmarks, showing significant improvements relative to several state-of-the-art collaborative filtering and graph neural network-based recommendation models. Further experiments quantitatively verify the effectiveness of each component of our proposed model and demonstrate that the learned embeddings capture the important relationship structure.

I. INTRODUCTION

The introduction identifies limitations in existing recommendation models and presents Multi-GCCF, which combines type-specific graph processing with explicit user-user and item-item relationships. Experiments on four real-world datasets report superiority over state-of-the-art models.

  • I. INTRODUCTION: Existing deep learning recommendation models may learn suboptimal embeddings because they use user and item features without explicitly incorporating interactions during embedding construction.The introduction also notes their reliance on relatively sparse explicit feedback.
  • I. INTRODUCTION: Recent bipartite-graph methods improve recommendation but use aggregation functions that do not depend on whether a node is a user or an item.The paper motivates type-dependent aggregation and transformation as a response to this limitation.
  • I. INTRODUCTION: Multi-GCCF applies separate aggregation and transformation functions to user and item nodes, addressing their intrinsic difference in graph convolution.The paper reports that this improves embedding precision and recommendation performance.
  • I. INTRODUCTION: Multi-GCCF jointly learns from user-item, user-user, and item-item graphs through a multi-graph encoding layer.The three graphs provide complementary relationship information for embedding learning.
  • I. INTRODUCTION: Experiments on four real-world datasets containing more than one million user-item interactions demonstrate Multi-GCCF's superiority over strong state-of-the-art models.The evidence reports the dataset scale and overall comparison but does not provide specific metric values.

II. RELATED WORK

Related work progresses from model-based collaborative filtering to neural and graph-based approaches. The paper's method builds on this trajectory by encoding user-item interactions together with user-user and item-item similarity graphs.

  • II. RELATED WORK: Matrix factorization represents users and items as vectors inferred from observed user-item interactions, while neural models capture more complex similarity relationships.These approaches form the model-based foundation preceding graph neural recommendation methods.
  • II. RELATED WORK: Graph methods represent pairwise recommendation relationships using user-item interaction graphs, with newer work applying graph neural networks to recommendation.Examples include graph convolutional matrix completion and PinSage.
  • II. RELATED WORK: Multi-GCCF extends graph-based collaborative filtering with a Bipar-GCN encoder, a multi-graph encoding layer, and a skip connection.The method processes the user-item graph alongside graphs representing user-user and item-item similarities.

A. Bipartite Graph Convolutional Neural Networks

Bipar-GCN encodes users and items from the bipartite interaction graph by sampling neighborhoods and aggregating multi-hop information with node-type-specific transformations.

  • A. Bipartite Graph Convolutional Neural Networks: Forward sampling addresses long-tailed degree distributions before backward aggregation processes the sampled neighborhoods.Popular items may have many user interactions, motivating the sampling phase.
  • A. Bipartite Graph Convolutional Neural Networks: Bipar-GCN encodes user and item nodes by iteratively aggregating k-hop neighborhood information in the bipartite interaction graph.Initial user and item embeddings are learned, optionally from informative node features.
  • A. Bipartite Graph Convolutional Neural Networks: User and item nodes use separate transformation and aggregation weights, reflecting their intrinsic difference in the bipartite graph.The user transformation matrix is shared across user nodes, while item nodes use another parameter set.
  • A. Bipartite Graph Convolutional Neural Networks: A weighted-mean neighborhood aggregator provides permutation-invariant representations for user neighborhoods.The neighborhood embedding is learned from neighboring node representations.

B. Multi-Graph Encoding Layer

The Multi-Graph Encoding layer supplements the bipartite graph with user-user and item-item similarity graphs to capture proximal relationships and alleviate interaction sparsity.

  • B. Multi-Graph Encoding Layer: MGE constructs user-user and item-item graphs from cosine similarities in the rating or click matrix.These graphs capture proximity among users and items beyond the user-item interaction graph.
  • B. Multi-Graph Encoding Layer: The additional graphs provide proximity information that can compensate for sparsity in the user-item interaction graph.MGE merges its outputs with Bipar-GCN representations to exploit dependencies encoded by all three graphs.
  • B. Multi-Graph Encoding Layer: One-hop graph convolution with a sum aggregator generates additional embeddings from the neighborhoods of target users and items.The layer uses learnable user and item aggregation weight matrices.
  • B. Multi-Graph Encoding Layer: MGE uses no additional neighbor sampling and sets similarity thresholds to produce an average degree of 10 for each graph.

C. Skip-connection with Original Node Features

Skip connections preserve information from original node features alongside relationship-based embeddings, after which multiple representations are fused into one vector.

  • C. Skip-connection with Original Node Features: Skip connections re-emphasize original node features whose influence may diminish when graph layers extract relationship-based information.The original features pass through a single fully connected layer to form skip-connection embeddings.
  • C. Skip-connection with Original Node Features: The model investigates element-wise summation, concatenation, and attention for merging embeddings from three perspectives.These perspectives are represented by Bipar-GCN, MGE, and skip connections.
  • C. Skip-connection with Original Node Features: Table I compares the model's alternative message-fusion methods.

E. Model Training

Multi-GCCF trains on mini-batches of user-positive-item-negative triplets, producing fused embeddings optimized with Bayesian Personalized Ranking and regularization.

  • E. Model Training: Mini-batch training selects unique users and items from triplet pairs and obtains their embeddings after information fusion.The embeddings are optimized with stochastic gradient descent.
  • E. Model Training: The BPR objective uses observed positive interactions and sampled unobserved negative interactions in the training batch.The model scores user-item pairs using the learned embeddings.
  • E. Model Training: Regularization is applied to model parameters and generated embeddings to prevent overfitting.The regularization coefficients are λ and β.

IV. EXPERIMENTAL EVALUATION

The evaluation compares Multi-GCCF with collaborative filtering and graph neural network baselines on four real-world datasets using Recall@20 and NDCG@20.

  • IV. EXPERIMENTAL EVALUATION: Experiments evaluate Multi-GCCF against classical collaborative filtering and graph neural network methods on four benchmark datasets.The datasets are Gowalla, Amazon-Books, Amazon-CDs, and Yelp2018.
  • IV. EXPERIMENTAL EVALUATION: Recall@20 measures coverage of preferred items in top-k recommendations, while NDCG@20 measures ranking quality.
  • IV. EXPERIMENTAL EVALUATION: Multi-GCCF uses two convolution layers on the user-item graph and one layer on each user-user and item-item graph.These components model high-order interaction information and user-item or item-item similarities.

C. Parameter Settings

The experiments use standardized optimization and embedding settings, compare overall performance in Table II, and include dataset and ablation-study references.

  • C. Parameter Settings: All models use Adam optimization, Xavier initialization, embedding size 64, and batch size 1024, with grid search for learning rate and L2 regularization.Dropout rate and network structure are additionally tuned for GC-MC and NGCF, with pre-training used for NGCF and GC-MC.
  • C. Parameter Settings: Overall performance is reported in Table II, with each result averaged across five runs using random weight initializations.
  • C. Parameter Settings: The evaluation uses publicly accessible real-world datasets with varied domains, sizes, and sparsity, while Table IV reports ablation studies.

E. Ablation Analysis

Ablation experiments show that Bipar-GCN, multi-graph encoding, and skip connections each contribute to performance, while summation is the strongest tested fusion method.

  • E. Ablation Analysis: Bipar-GCN substantially improves performance with one convolution layer on each side, while additional layers provide only slight gains.
  • E. Ablation Analysis: Both the MGE layer and skip connections produce significant performance improvements in the ablation analysis.
  • E. Ablation Analysis: All three main components—Bipar-GCN, MGE, and skip connections—are effective, and combining them yields further improvement.The combined embeddings capture different information about users, items, and user-item relationships.
  • E. Ablation Analysis: Summation outperforms concatenation and attention for fusing the three embeddings in the tested Gowalla and Amazon-CDs experiments.Summation preserves the component dimension and adds no learnable parameters.

G. Embedding Visualization

Multi-GCCF produces tighter item-embedding clusters for items preferred by the same user than BPRMF. The paper attributes this visualization to a multi-graph collaborative-filtering model whose components are supported by ablation results.

  • G. Embedding Visualization: The visualization includes item embeddings from users’ clicked or visited histories, including test items unobserved during training.Nodes sharing a color represent the item embeddings associated with one user's history.
  • G. Embedding Visualization: Multi-GCCF generates tighter clusters for items preferred by the same user than BPRMF.Both methods place items from the same user's history near one another, but Multi-GCCF shows stronger grouping.
  • G. Embedding Visualization: Multi-GCCF incorporates user-item, user-user, and item-item relationships through multiple graph-based embeddings.The broader model description explains the relationship structure represented by the visualization.
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