每日一佳——Structure Preserving Embedding（Blake Shaw et al. ，ICML，2009）
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题目意思：结构保存嵌入，也就是“保存结构信息的图嵌入算法”，等等，什么是图嵌入？1.A graph embedding is a particular drawing of a graph. 2.Graph Embedding in Vector Spaces
2009年的这篇Best Paper可以说是关于计算机视觉的。
摘要：Structure Preserving Embedding (SPE) is an algorithm for embedding graphs in Euclidean space such that the embedding is low-dimensional and preserves the global topological properties of the input graph.Topology is preserved if a connectivity algorithm, such as k-nearest neighbors, can easily recover the edges of the input graph from only the coordinates of the nodes after embedding. SPE is formulated as a semidefinite program that learns a low-rank kernel matrix constrained by a set of linear inequalities which captures the connectivity structure of the input graph. Traditional graph embedding algorithms do not preserve structure according to our definition, and thus the resulting visualizations can be misleading or less informative. SPE provides significant improvements in terms of visualization and lossless compression of graphs, outperforming popular methods such as spectral embedding and Laplacian eigen-maps. We find that many classical graphs and networks can be properly embedded using only a few dimensions. Furthermore, introducing structure preserving constraints into dimensionality reduction algorithms produces more accurate representations of high-dimensional data.
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