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Bundle Recommendation with Graph Convolutional Networks

Jianxin Chang, Chen Gao, Xiangnan He, Yong Li, Depeng Jin

arXiv:2005.03475v1cs.IRcs.LG

TL;DR

Bundle recommendation must account for item and bundle relationships while addressing existing approaches’ limited modeling of affiliation and bundle-choice decisions. BGCN represents these relationships in a heterogeneous graph and trains with hard negatives; it outperforms state-of-the-art baselines on two real-world datasets by 10.77% to 23.18%.

  • Problem

    Existing bundle-recommendation approaches use parameter sharing or multi-task learning but do not explicitly model item-bundle affiliation or users’ decisions between bundles.

    Source: §1 · p. 1

  • Method

    BGCN unifies user-item interactions, user-bundle interactions, and bundle-item affiliations in a heterogeneous graph, then uses hard-negative samples during training.

    Source: §1 · p. 1, §3.5 · p. 3

  • Results

    10.77% to 23.18%: BGCN outperforms existing state-of-the-art baselines on two real-world datasets.

    Source: §1 · p. 1

  • Takeaways & Limitations

    Experiments on real-world datasets demonstrate BGCN’s effectiveness for bundle recommendation.

    Source: §6 · p. 4

    The problem formulation assumes user-bundle interactions, user-item interactions, and bundle-item affiliation data as inputs.

    Source: §2 · p. 2

Abstract

from arXiv · show

Bundle recommendation aims to recommend a bundle of items for a user to consume as a whole. Existing solutions integrate user-item interaction modeling into bundle recommendation by sharing model parameters or learning in a multi-task manner, which cannot explicitly model the affiliation between items and bundles, and fail to explore the decision-making when a user chooses bundles. In this work, we propose a graph neural network model named BGCN (short for \textit{\textBF{B}undle \textBF{G}raph \textBF{C}onvolutional \textBF{N}etwork}) for bundle recommendation. BGCN unifies user-item interaction, user-bundle interaction and bundle-item affiliation into a heterogeneous graph. With item nodes as the bridge, graph convolutional propagation between user and bundle nodes makes the learned representations capture the item level semantics. Through training based on hard-negative sampler, the user's fine-grained preferences for similar bundles are further distinguished. Empirical results on two real-world datasets demonstrate the strong performance gains of BGCN, which outperforms the state-of-the-art baselines by 10.77\% to 23.18\%.

1 Introduction

Bundle recommendation must account for item composition and the sparse user-bundle interactions that result when users need to like most items in a bundle. BGCN models user, item, and bundle relationships in a heterogeneous graph and uses hard negatives to distinguish similar bundles.

1 Introduction

  • Existing approaches share parameters or transfer item-task benefits, but do not explicitly model user-item-bundle relations or users’ decisions between similar bundles.For similar bundles, non-overlapping parts can determine the user's final choice; a single disliked item can also lead a user to refuse a bundle.Source: §1 · p. 1
  • BGCN unifies user, item, and bundle nodes in a heterogeneous graph, using items as a bridge for user-bundle propagation and a bundle-item-bundle meta-path for bundle alternatives.Hard-negative training further explores users’ decision-making when choosing bundles.Source: §1 · p. 1
  • 10.77% to 23.18%: BGCN outperforms existing state-of-the-art baselines on two real-world datasets.The contribution summary reports this range without assigning its endpoints to specific datasets or metrics.Source: §1 · p. 1
  • The authors describe BGCN as the first graph neural network model, to their knowledge, to explicitly model complex user, item, and bundle relations for bundle recommendation.They also report two-level embedding propagation that incorporates item-level information into user and bundle representations and distinguishes fine-grained bundle differences through hard negatives.Source: §1 · p. 1

2 Problem Definition

The problem formulation takes user-bundle interactions, user-item interactions, and bundle-item affiliations as input. It outputs a model that estimates the probability that a user will interact with a bundle.

2 Problem Definition

  • The bundle-item affiliation matrix marks whether each item belongs to each bundle, while the two interaction matrices record observed user-bundle and user-item interactions.The entries are binary; an affiliation entry of 1 means the bundle contains that item.Source: §2 · p. 1
  • The formulation takes user-bundle interaction, user-item interaction, and bundle-item affiliation data as input.The passage defines these data as binary matrices over users, bundles, and items.Source: §2 · pp. 1–2
  • The output is a recommendation model that estimates the probability that user u will interact with bundle b.Source: §2 · p. 2

3 Methodology

BGCN models users, items, and bundles in one heterogeneous graph and propagates information across item and bundle levels. It uses overlap-aware bundle propagation and hard-negative training to represent bundle alternatives and users’ fine-grained choices.

3.1 Heterogeneous Graph Construction

  • BGCN constructs an undirected heterogeneous graph linking users to bundles and items, and bundles to their constituent items.One-hot node features are projected into dense embeddings.Source: §3.1 · p. 2

3.2 Item Level Propagation

  • User–item propagation captures item preferences, while pooling item information into bundles captures their item-level semantics.The authors use mean aggregation and note that this mechanism may weaken the effect of sparse bundle data and naturally improve cold-start capability.Source: §3.2 · p. 2

3.3 Bundle Level Propagation

  • Bundle-level propagation models user preferences and bundle attributes, using normalized item overlap on the bundle-item-bundle meta-path to represent alternatives.Bundles sharing more items are treated as more similar.Source: §3.3 · p. 2

3.4 Prediction

  • After L propagation iterations, BGCN concatenates embeddings from different depths and combines item- and bundle-level representations for final prediction.The prediction uses an inner product.Source: §3.4 · pp. 2–3

3.5 Training with Hard Negatives

  • BGCN trains with pairwise learning, then introduces hard negatives probabilistically after convergence to model users’ bundle choices.A hard negative is an unobserved bundle whose items the user has mostly interacted with, or one that overlaps the positive bundle.Source: §3.5 · p. 3

4 Experiments

Experiments on Netease and Youshu evaluate BGCN against state-of-the-art methods, test its key designs, and examine performance under data sparsity.

4 Experiments

  • The evaluation is organized around benchmark comparison, ablations of key designs, and performance across user groups with different sparsity levels.The three research questions ask how BGCN compares with state-of-the-art methods, how its designs affect performance, and how it performs under sparsity.Source: §4 · p. 3

4.1 Experimental Settings

  • Netease music and Youshu book bundles are evaluated with Recall@K and NDCG@K, which measure top-K hit coverage and rank-sensitive hit quality, respectively.The experiments compare six baselines, including graph-based and multi-task methods, and use hard-negative sampling with an 80% probability.Source: §4.1.1 · p. 3

4.2 Overal Performance (RQ1)

  • The graph baselines outperform MFBPR but do not exceed DAM, while tripartite GCN-TG and NGCF-TG do not always beat their bipartite counterparts.The authors attribute this pattern to models’ inability to distinguish item-bundle affiliation, which can make added item input noisy.Source: §4.2 · p. 3
  • 19.65%–23.18% on Netease and 10.77%–12.36% on Youshu: BGCN outperforms the best baseline across the reported comparisons.The authors report that BGCN achieves the best Recall and NDCG results on both datasets.Source: §4.2 · p. 3, Table 2 · p. 4

4.3 Ablation Study (RQ2)

  • Two-level propagation outperforms bundle-level-only propagation by 9.36%–11.57% on Netease and 2.75%–11.39% on Youshu.The ablation compares item-level-only, bundle-level-only, and two-level propagation.Source: §4.3 · p. 3, Table 3 · p. 4
  • 5.84%–6.74% on Netease and 1.79%–9.02% on Youshu: overlap-based bundle-to-bundle propagation improves performance.The authors report that this propagation helps extract bundle correlations, especially when overlap degree is included.Source: Table 3 · p. 4, §4.3 · p. 4
  • 9.26%–10.64% on Netease and 3.95%–11.78% on Youshu: hard-negative sampling improves performance over simple sampling.The comparison includes hard negatives at item level, bundle level, and both levels; the authors report particular benefit from using both.Source: Table 3 · p. 4, §4.3 · p. 4

4.4 Impact of Data Sparsity (RQ3)

  • For Netease users with 0–3 purchase records, BGCN reaches Recall@40 of 0.069 and NDCG@40 of 0.023, beating NGCF-TG by 30.19% and 27.78%, respectively.The performance gap between BGCN and other methods generally widens as data become sparser, except for NGCF-TG, which is very similar to BGCN.Source: §4.4 · p. 4

5 Related Work

Prior bundle-recommendation work linked item and bundle signals through shared parameters or multi-task learning. Related GCN work developed graph-based recommendation methods, but these passages describe no prior GCN approach specifically for bundle recommendation.

5 Related Work

  • LIRE and EFM use users’ item and bundle interactions under BPR, BBPR reuses parameters learned by item BPR, and DAM jointly models item and bundle interactions through multi-task learning.Source: §5 · p. 4
  • GCN recommendation work progresses from rating-matrix factorization to web-scale neighbor sampling and higher-order connectivity for collaborative filtering.Source: §5 · p. 4

6 Conclusions and Future Work

BGCN represents user–item and user–bundle interactions and item–bundle affiliation in a graph, and experiments on real-world datasets demonstrate its effectiveness. Future work will consider discount factors in bundle recommendation.

  • BGCN reconstructs user–item and user–bundle interactions plus item–bundle affiliation in a graph.Source: §6 · p. 4
  • Experiments on real-world datasets demonstrate the effectiveness of the graph-based solution.Source: §6 · p. 4
  • Future work will consider the discount factor in bundle recommendation.Source: §6 · p. 4
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