1 / 13

Structure Preserving Embedding

Structure Preserving Embedding. Blake Shaw, Tony Jebara ICML 2009 (Best Student Paper nominee) Presented by Feng Chen. Outline. Motivation Solution Experiments Conclusion. Motivation.

ronda
Download Presentation

Structure Preserving Embedding

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Structure Preserving Embedding Blake Shaw, Tony Jebara ICML 2009 (Best Student Paper nominee) Presented by Feng Chen

  2. Outline • Motivation • Solution • Experiments • Conclusion

  3. Motivation • Graphs exist everywhere: web link networks, social networks, molecules networks, k-nearest neighbor graph, and more. • Graph Embedding • Embed a graph in a low dimensional space. • What used for? Visualization, Compression, and More. • Existing methods: Planar Embedding (no crossing arcs); Spectral Embedding (preserve local distances); LaplacianEigenmaps (preserve local distances).

  4. Problem Statement • Given only the connectivity of a graph, can we efficiently recover low-dimensional point coordinates for each node such that these points can be easily used to reconstruct the original structure of the network?

  5. Optimization Formulation

  6. Justifications • Why can preserve the local distances?

  7. Justifications • Interpret the slack variable 

  8. Implementation • It is about finding a positive semi-definite matrix that can maximize an objective function, subject to some constraints about the matrix. • This category of optimization problem is called “Semi-definite Programming” • Available MATLAB tools include CSDP and SDP-LR.

  9. Related Work • Spectral Embedding • Find the d leading eigen-vectors of the adjacency matrix A as the coordinates. • LaplacianEigenmaps • Employ a spectral decomposition of the graph Laplacian L=D-A, where D=diag(A1), and use the d eigenvectors of L with the smallest nonzero eigenvalues. • Look weird? But this approach has the fundamental from manifold theories in the field of topology!!

  10. Experiments

  11. Experiment

  12. Conclusion • Innovative idea! • Technically simple!

  13. Thank You! Any Question?

More Related