Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Training structural SVMs when exact inference is intractable
Proceedings of the 25th international conference on Machine learning
Language pyramid and multi-scale text analysis
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
Learning an affine transformation for non-linear dimensionality reduction
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
A Family of Simple Non-Parametric Kernel Learning Algorithms
The Journal of Machine Learning Research
Metric Learning for Estimating Psychological Similarities
ACM Transactions on Intelligent Systems and Technology (TIST)
Improving fuzzy multilevel graph embedding through feature selection technique
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
A distributed algorithm for large-scale generalized matching
Proceedings of the VLDB Endowment
Large-scale SVD and manifold learning
The Journal of Machine Learning Research
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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.