Multiplex Heterogeneous Graph Convolutional Network

1 INTRODUCTION

• Attributed multiplex heterogeneous networks combine multi-typed nodes, multiple relations between node pairs, and node attributes.The introduction distinguishes node-type heterogeneity from relation multiplicity, using user-item interactions as an example.Source: §1 · pp. 1–2
• Existing methods face challenges in automatically learning meta-path dependencies, encoding relation heterogeneity and multiplexity, and scaling to large networks.The paper identifies high time complexity and memory consumption as limits of many current methods.Source: §1 · p. 2
• MHGCN combines multiplex relation aggregation and multilayer graph convolution to learn relation-aware representations and meta-path interactions of different lengths.The framework also integrates node attributes and uses simplified convolution for feature aggregation.Source: §1 · p. 2
• MHGCN is reported to outperform state-of-the-art baselines on five real-world datasets for link prediction and node classification.The paper also reports efficiency improvements of up to two orders of magnitude over state-of-the-art GNN baselines for attributed multiplex heterogeneous networks.Source: §1 · p. 2

Graph Neural Networks

• Homogeneous-network GNNs use neighborhood aggregation, attention, relation-specific modeling, or simplified convolution, but do not preserve heterogeneous and multiplex graph characteristics.The section describes Kipf et al., GraphSAGE, GAT, R-GCN, LightGCN, and AM-GCN.Source: §2 · p. 2

Heterogeneous Graph Representation

• Heterogeneous graph methods encode node and edge context, but many rely on selecting useful meta-paths, sometimes requiring external domain knowledge.Examples include metapath2vec, HERec, HetGNN, HeGAN, NARS [38], and Fu et al..Source: §2 · p. 2
• Although HGT models dynamic dependencies with self-attention and HPN aggregates node embeddings across metapaths, most heterogeneous graph embedding models ignore multiplex relational context involving multiple relationship types between nodes.Multiplex approaches include MNE, GATNE, DMGI, and HGSL, but their generality is limited by manual meta-path construction.Source: §2 · p. 3

Multiplex Heterogeneous Network Embedding

• Other multiplex approaches include FAME, DualHGCN, and HDI, with FAME trading adaptive parameter learning for fast embedding projection.DualHGCN uses homogeneous hypergraphs and spectral hypergraph convolutions; HDI uses high-order mutual information for supervision signals.Source: §2 · p. 3

3 PROBLEM DEFINITION

• An attributed multiplex heterogeneous network associates node attribute vectors with a graph whose nodes and edges have types, allowing multiple typed edges between the same pair of nodes.The definition denotes node- and edge-type mappings by φ and ψ, respectively.Source: §3 · p. 3
• A meta-path describes a composite relation between node types through a sequence of relations.The relation composition is denoted by ◦.Source: §3 · p. 3
• The representation-learning objective is a low-dimensional embedding for each node that preserves node and edge heterogeneity and multiplexity.The stated hidden dimensionality d_d is much smaller than the number of nodes |V|.Source: §3 · p. 3

4.1 Multiplex Relation Aggregation

• Trainable relation-aware weights aggregate edge-type-specific subgraph adjacency matrices so different relations contribute with learned importance.The weights are learned during training rather than set as hyperparameters.Source: §4.1 · p. 4

4.2 Multilayer Graph Convolution Module

• Layerwise convolution and fusion automatically capture different-length meta-paths across relations, avoiding manual path selection and sampling.The convolution omits nonlinear activation, following a simplified GCN.Source: §4.2 · pp. 4–5

4.3 Model Learning

• MHGCN supports unsupervised training with negative-sampled binary cross-entropy and semi-supervised training with cross-entropy over labeled nodes.In semi-supervised learning, a small fraction of labeled nodes guides optimization for node classification.Source: §4.3 · p. 5

5.1 Datasets; 5.3 Experimental Setting

• Experiments used five real-world datasets: Alibaba, Amazon, AMiner, IMDB, and DBLP; Alibaba results came from a sampled dataset.Training rounds were set to 500 for link prediction and 200 for node classification.Source: §5.1 · p. 6, §5.3 · p. 6

5.2 Baselines

• Eighteen baselines span homogeneous, heterogeneous, and multiplex network embedding methods, including node2vec, HAN, and GATNE.The compared methods were grouped into three categories.Source: §5.2 · p. 6

5.4 Link Prediction; 5.5 Node Classification

• 5.68% average F1 gain over the best GNN baselines on link prediction; node classification gains averaged 11.22% Macro-F1 and 14.49% Micro-F1 over HGSL.MHGCN also achieved state-of-the-art performance on all tested networks in node classification.Source: Table 2 · p. 7, §5.4 · p. 7, §5.5 · p. 7

5.6 Ablation Study

• MHGCN-R’s fixed relation weights reduced Alibaba Macro-F1 by 9.68%; multilayer convolution improved Macro-F1 by 2.97%, 18.98%, 4.09%, and 1.51% on AMiner, Alibaba, IMDB, and DBLP.The ablation results attribute improvements to both relation weighting and multilayer convolution.Source: Figure 3 · p. 7, §5.6 · p. 8

5.7 Parameter Sensitivity

• Two graph layers achieved the best performance, embedding dimension 128 was best, and performance stabilized within 80 training rounds across tested datasets.The study reports Macro-F1 for node classification on four datasets; Alibaba uses the right-hand ordinate in Figure 4.Source: §5.7 · pp. 8–9, Figure 4 · p. 8

• Experiments on five real-world heterogeneous networks show MHGCN's superiority across different graph representation tasks.Source: §6 · p. 9
• Multiplex relation aggregation distinguishes the importance of relations between nodes in multiplex heterogeneous networks.Source: §6 · p. 9
• The multilayer graph convolution module automatically captures short and long meta-path interactions across multiple relations.The model learns node embeddings through parameter learning during training.Source: §6 · p. 9

• The paper identifies Table 4 as the location of definitions for its key notations.Source: §A.1 · p. 10
• Table 4 summarizes the paper's key notations.Source: Table 4 · p. 10

• The procedure takes generated AMHEN G and node feature matrix X as input and outputs graph node embeddings H.Source: §A.2 · p. 10
• It decouples the AMHEN into homogeneous and bipartite graphs to generate relation-specific adjacency matrices.Source: §A.2 · p. 10
• The procedure calculates A as the weighted sum of relation-specific adjacency matrices using weights β_r.Source: §A.2 · p. 10
• It calculates learning objective L using Eq. (6) or Eq. (7), then backpropagates to update MHGCN parameters.Source: §A.2 · p. 10

• Alibaba uses four user-item interaction types as multiplex relations and item categories as node-classification labels; Amazon uses co-viewing and co-purchasing edges with product attributes.Amazon product features include category, sales-rank, brand, and price.Source: §A.3 · p. 10
• AMiner includes author, paper, and conference nodes with paper-domain labels; IMDB uses movie, director, and actor nodes, movie genres as labels, and bag-of-words features.Source: §A.3 · p. 10
• DBLP includes author, paper, venue, and term nodes, with authors' research fields used as node-class labels.Source: §A.3 · p. 10

A.4 Detailed Experimental Settings

• Link prediction uses connected pairs as positives and an equal number of sampled unlinked pairs as negatives; node classification uses logistic regression, and results average 10 runs.For link prediction, edge types are predicted using all edge types, and results are averaged across edges.Source: §A.4 · p. 10
• MHGCN uses 2 convolution layers, learning rate 0.05, dropout 0.5, and weight decay 0.0005.The reported setup also uses 500 training rounds for link prediction and 200 for node classification.Source: §A.4 · p. 10

A.5 Baselines

• Homogeneous and heterogeneous embedding baselines receive separate single-view graphs, whose embeddings are mean-pooled; DualHGNN is evaluated only on Alibaba.Table 5 summarizes the graph types handled by the baselines.Source: §A.5 · p. 11, Table 5 · p. 11

A.6.1 Model Efficiency Analysis.

• MHGCN achieves fourth-best performance after R-GCN, NARS, and HPN, while remaining significantly faster than HGSL on all datasets.Table 6 reports runtime comparisons of GNN methods.Source: §A.6.1 · p. 11, Table 6 · p. 11
• MHGCN is up to 135× faster than HAN, 21.25× faster than GTN on Alibaba, and 2.33× and 16.58× faster than MAGNN on Alibaba and AMiner.It converges within 80 rounds for node classification on four tested datasets; the authors attribute its efficiency to omitting nonlinear activation.Source: §A.6.1 · p. 11