Summary A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach, called network-supervised dimension reduction, in which covariates are projected onto low-dimensional spaces to reveal the linkage pattern without assuming a model. We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer proximity in the low-dimension projection corresponds to stronger connections. Interestingly, the convergence rate of our estimator is found to depend on a network effect factor, which is the smallest number that can partition a graph in a manner similar to the graph colouring problem. Our method has interesting connections to principal component analysis and linear discriminant analysis, which we exploit for clustering and community detection. The proposed approach is further illustrated by numerical experiments and analysis of a pulsar candidates dataset from astronomy.

中文翻译：

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网络数据中协变量的降维

总结 网络数据分析的一个主要问题是使用上下文信息来解释连接的强度。为了实现这一点，我们引入了一种称为网络监督降维的新方法，其中协变量被投影到低维空间以揭示链接模式而不假设模型。我们提出了一种新的损失函数来估计得到的线性投影中的参数，基于低维投影中更接近对应于更强连接的概念。有趣的是，我们的估计器的收敛速度被发现取决于网络效应因子，这是可以以类似于图着色问题的方式划分图的最小数字。我们的方法与主成分分析和线性判别分析有有趣的联系，我们将其用于聚类和社区检测。所提出的方法通过数值实验和对天文学脉冲星候选数据集的分析进一步说明。