标题： 批量核SOM及相关拉普拉斯方法在社会网络分析中的应用 显示英文标题

标题： Batch kernel SOM and related Laplacian methods for social network analysis

摘要： 大型图是描述众多领域中数据结构的自然数学模型，例如网络挖掘、社交网络、信息检索、生物网络等。 对于所有这些应用，都需要自动工具来获取图的综合视图，并深入理解潜在问题。 特别是，在实践中发现紧密连接的顶点组及其之间的关系非常重要。 本文展示了如何通过基于图的拉普拉斯矩阵衍生出的核函数，使用批量自组织映射的核版本来实现这些目标，尤其是在将其与基于图谱分析的经典方法结合使用时。 所提出的方法被用于探索一个从中世纪社会网络衍生出的加权图的结构，该网络通过从大量农业合同语料库直接构建而成。 显示英文摘要

摘要： Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts.