The relationships between objects in a network are typically diverse and complex, leading to the heterogeneous edges with different semantic information. In this article, we focus on exploring the heterogeneous edges for network representation learning. By considering each relationship as a view that depicts a specific type of proximity between nodes, we propose a multi-stage non-negative matrix factorization (MNMF) model, committed to utilizing abundant information in multiple views to learn robust network representations. In fact, most existing network embedding methods are closely related to implicitly factorizing the complex proximity matrix. However, the approximation error is usually quite large, since a single low-rank matrix is insufficient to capture the original information. Through a multi-stage matrix factorization process motivated by gradient boosting, our MNMF model achieves lower approximation error. Meanwhile, the multi-stage structure of MNMF gives the feasibility of designing two kinds of non-negative matrix factorization (NMF) manners to preserve network information better. The united NMF aims to preserve the consensus information between different views, and the independent NMF aims to preserve unique information of each view. Concrete experimental results on realistic datasets indicate that our model outperforms three types of baselines in practical applications.

中文翻译：

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用于探索异构边缘的多阶段网络嵌入

网络中对象之间的关系通常是多样和复杂的，导致具有不同语义信息的异构边缘。在本文中，我们专注于探索网络表示学习的异构边缘。通过将每个关系视为描述节点之间特定类型接近度的视图，我们提出了一种多阶段非负矩阵分解（MNMF）模型，致力于利用多个视图中的丰富信息来学习鲁棒的网络表示。事实上，大多数现有的网络嵌入方法都与隐式分解复杂的邻近矩阵密切相关。然而，近似误差通常很大，因为单个低秩矩阵不足以捕获原始信息。通过梯度提升驱动的多阶段矩阵分解过程，我们的 MNMF 模型实现了较低的近似误差。同时，MNMF的多级结构为设计两种非负矩阵分解（NMF）方式以更好地保存网络信息提供了可行性。统一的 NMF 旨在保存不同视图之间的共识信息，而独立的 NMF 旨在保存每个视图的唯一信息。在实际数据集上的具体实验结果表明，我们的模型在实际应用中优于三种基线。MNMF的多级结构为设计两种非负矩阵分解（NMF）方式以更好地保存网络信息提供了可行性。统一的 NMF 旨在保存不同视图之间的共识信息，而独立的 NMF 旨在保存每个视图的唯一信息。在实际数据集上的具体实验结果表明，我们的模型在实际应用中优于三种基线。MNMF的多级结构为设计两种非负矩阵分解（NMF）方式以更好地保存网络信息提供了可行性。统一的 NMF 旨在保存不同视图之间的共识信息，而独立的 NMF 旨在保存每个视图的唯一信息。在实际数据集上的具体实验结果表明，我们的模型在实际应用中优于三种基线。