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Blake Shaw

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2 papers

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NeurIPS Conference 2011 Conference Paper

Learning a Distance Metric from a Network

Blake Shaw
Bert Huang
Tony Jebara

Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding algorithm structure preserving embedding, SPML learns a metric which is structure preserving, meaning a connectivity algorithm such as k-nearest neighbors will yield the correct connectivity when applied using the distances from the learned metric. We show a variety of synthetic and real-world experiments where SPML predicts link patterns from node features more accurately than standard techniques. We further demonstrate a method for optimizing SPML based on stochastic gradient descent which removes the running-time dependency on the size of the network and allows the method to easily scale to networks of thousands of nodes and millions of edges.

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ICML Conference 2009 Conference Paper

Structure preserving embedding

Blake Shaw
Tony Jebara

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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