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arXiv 1805.07544stat.MLcs.ITcs.LGmath.IT
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条件网络嵌入

Conditional Network Embeddings

Ghent University(根特大学)

Bo Kang, Jefrey Lijffijt, Tijl De Bie

摘要:

网络嵌入(NE)将给定网络的节点映射到$d$维欧氏空间$\mathbb{R}^d$中。理想情况下,这种映射使得“相似”节点被映射到附近的点上,使得NE可以用于诸如链路预测(如果“相似”意味着“更可能被连接”)或分类(如果“相似”意味着“更可能具有相同的标签”)之类的目的。近年来,已经引入了各种NE方法,所有方法都遵循类似的策略:定义节点之间的相似性概念(通常是网络内的距离度量),嵌入空间中的距离度量,以及惩罚相似节点的大距离和不相似节点的小距离的损失函数。现有方法面临的困难是,某些网络由于其结构特性而从根本上难以嵌入:为了克服这一点,我们引入了一个概念创新的NE文献,并提出创建\emph{Conditional Network Embeddings}(CNEs);嵌入最大程度地增加关于给定结构属性(例如,节点度、块密度等)的信息。我们使用一个简单的贝叶斯方法来实现这一点,并提出了一个块随机梯度下降算法来有效地拟合它。我们证明,CNE是优越的链接预测和多标签分类相比,国家的最先进的方法,这不会增加显着的数学或计算复杂性。最后,我们说明了CNE网络可视化的潜力。

英文摘要:

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or classification (if `similar' means `being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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