论文标题
一个基于Pagerank的柔性图形嵌入框架与光谱特征向量嵌入密切相关
A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings
论文作者
论文摘要
我们研究了一种基于播种在随机节点上的个性化Pagerank矢量矩阵的简单嵌入技术。 We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral embedding for a class of graphs where spectral embeddings are significant, and hence useful representation of the data, (2) can be done for the entire network or a smaller part of it, which enables precise local representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks.最重要的是，这种嵌入策略的一般性质为基于Pagerank的亲戚提供了许多新兴应用，在这些应用程序中，特征向量和光谱技术可能无法得到很好的确定。例如，类似的技术可以在来自HyperGraphs的Pagerank载体上使用，以获取“光谱”样嵌入。
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral embedding for a class of graphs where spectral embeddings are significant, and hence useful representation of the data, (2) can be done for the entire network or a smaller part of it, which enables precise local representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks. Most importantly, the general nature of this embedding strategy opens up many emerging applications, where eigenvector and spectral techniques may not be well established, to the PageRank-based relatives. For instance, similar techniques can be used on PageRank vectors from hypergraphs to get "spectral-like" embeddings.
