A Latent Space Model for Weighted Keyword Co-Occurrence Networks with Applications in Knowledge Discovery in Statistics

Keywords are widely recognized as pivotal in conveying the central idea of academic articles. In this article, we construct a weighted and dynamic keyword co-occurrence network and propose a latent space model for analyzing it. Our model has two special characteristics. First, it is applicable to weighted networks; however, most previous models were primarily designed for unweighted networks. Simply replacing the frequency of keyword co-occurrence with binary values would result in a significant loss of information. Second, our model can handle the situation where network nodes evolve over time, and assess the effect of new nodes on network connectivity. We use the projected gradient descent algorithm to estimate the latent positions and establish the theoretical properties of the estimators. In the real data application, we study the keyword co-occurrence network within the field of statistics. We identify popular keywords over the whole period as well as within each time period. For keyword pairs, our model provides a new way to assess the association between them. Finally, we observe that the interest of statisticians in emerging research areas has gradually grown in recent years. Supplementary materials for this article are available online.

关键词是传递学术文章核心主旨的关键要素，这一点已得到广泛共识。本文构建了加权动态关键词共现网络，并提出了用于分析该网络的隐空间模型（latent space model）。该模型具备两项独特特性：其一，可适用于加权网络场景，而既往多数模型主要针对无权网络设计，若仅将关键词共现频次替换为二元取值，将造成信息的显著流失；其二，该模型能够处理网络节点随时间演化的情形，并可评估新增节点对网络连通性的影响。我们采用投影梯度下降算法（projected gradient descent algorithm）对隐位置进行估计，并确立了估计量的理论性质。在实际数据应用环节，我们针对统计学领域的关键词共现网络展开研究，识别出全时段以及各细分时段内的热门关键词。针对关键词对，本模型为评估二者间的关联提供了全新思路。最后我们发现，近年来统计学者对新兴研究领域的关注度逐步提升。本文的补充材料可在线获取。