图顶点之间的相似性度量
A measure of similarity between graph vertices
摘要：
本文引入了有向图顶点间相似度的概念。设G_A和G_B是两个有向图。我们定义了一个相似度矩阵，它的第（i，j）个实元素表示顶点j（在G_A中）与顶点i（在G_B中）的相似程度。相似矩阵可以作为线性变换的归一化偶迭代的极限而获得。在G_A=G_B=G的特殊情况下，矩阵是正方形，第（i，j）项是G的顶点i和j之间的相似性得分。我们指出，Kleinberg的“枢纽和权威”的方法来识别网页相关的一个给定的查询可以被看作是一个特殊的情况下，我们的定义的情况下，其中一个图有两个顶点和一个独特的有向边之间。在类似Kleinberg，我们表明，我们的相似性分数是由一个非负矩阵的主导特征向量的组件。我们的相似性概念的潜在应用是众多的。我们说明了一个应用程序的同义词自动提取单语词典。
英文摘要：
We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The similarity matrix can be obtained as the limit of the normalized even iterates of a linear transformation. In the special case where G_A=G_B=G, the matrix is square and the (i, j)-th entry is the similarity score between the vertices i and j of G. We point out that Kleinberg's "hub and authority" method to identify web-pages relevant to a given query can be viewed as a special case of our definition in the case where one of the graphs has two vertices and a unique directed edge between them. In analogy to Kleinberg, we show that our similarity scores are given by the components of a dominant eigenvector of a non-negative matrix. Potential applications of our similarity concept are numerous. We illustrate an application for the automatic extraction of synonyms in a monolingual dictionary.
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