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Graph Based Multi-Modality Learning

Graph Based Multi-Modality Learning. Hanghang Tong; Jingrui He Carnegie Mellon University Mingjing Li Microsoft Research Asia. Outline. Motivation Graph-based Semi-supervised learning Methods The Linear Fusion Scheme The Sequential Fusion Scheme Justifications Similarity Propagation

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Graph Based Multi-Modality Learning

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  1. Graph Based Multi-Modality Learning Hanghang Tong; Jingrui He Carnegie Mellon University Mingjing Li Microsoft Research Asia

  2. Outline • Motivation • Graph-based Semi-supervised learning • Methods • The Linear Fusion Scheme • The Sequential Fusion Scheme • Justifications • Similarity Propagation • Bayesian Interpretation • Graph-based un-supervised learning • Experimental Results • Conclusion ACM/Multimedia 2005

  3. Motivation • Multi-Modality in Multimedia • Video: • Digital Image: color vs. • Web Image: content vs. surrounding text • Traditional methods • Linear combination; super-kernel… • Co-Training… • Multi-view version of EM, DBSCAN… All Vector Model based ! ACM/Multimedia 2005

  4. Motivation (conts) • Two Key issues • How to learning within each modality • How to combine… • A more recent hot topic • Graph-based learning • Spectral Cluster; Eigen Map • Manifold Ranking… • Explore graph-based method in the context of multi-modality! ACM/Multimedia 2005

  5. Notation • n data points • c classes, • Two modalities: a and b • One Affinity Matrix for each modality: • for modality a (nxn) • for modality b (nxn) • Labeling Matrix: (nxc) • Vectorial Function: (nxc) • Learning task: • s ACM/Multimedia 2005

  6. Basic Idea • What is a ‘good’ vectorial function F? • As consistent as possible with • Info from modality a • Info from modality b • Info from Labeled points Y • How to? • Take into account the various constraints by optimization ACM/Multimedia 2005

  7. Linear Fusion Scheme Constrains. from modality b Constrains. from modality a • Optimization strategy • Optimization Solution • Iterative form • Closed form Constrains. from Labels Y Converge ACM/Multimedia 2005

  8. Sequential Fusion Scheme Constrains. from modality a and Y • Optimization strategy • Optimization Solution • Iterative form • Closed form Constrains. from modality b and Converge ACM/Multimedia 2005

  9. Similarity Propagation • Taylor expansion (linear fusion) • Similar result for sequential form Initial Label > Further propagate similarity by a and b; > Fuse the result by weighted sum > Propagate Y by a and b; > Fuse the result by weighted sum ACM/Multimedia 2005

  10. Bayesian Interpretation • Optimal F by MAP (linear form): • Assuming: • Conditional pdf • Prior by modality a • Prior by modality b • Fuse prior by • The above setting leads to… ACM/Multimedia 2005

  11. Extension to Un-Supervised Case • Compare • For one modality: • For two modalities (linear form): • Graph Laplacian Learning • Linear Form: • Sequential From: • Feed it the spectral cluster or embedding… Quite similar ! Independent on Y ! ACM/Multimedia 2005

  12. Experimental Results: Coral Image Sequential Form Linear Form Treat as one modality Color Hist Texture ACM/Multimedia 2005

  13. Experimental Results: Web Image Linear Form Sequential Form Treat as one modality Content Fea Surrounding Text ACM/Multimedia 2005

  14. Conclusion • Study multi-modality learning by graph based method • Propose two schemes for semi-supervised learning • Extend them to un-supervised learning ACM/Multimedia 2005

  15. Q&A The End Thanks ACM/Multimedia 2005

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