Presented by: Mingyuan Zhou Duke University, ECE September 17, 2010

1. Nonlinear Learning Using Local Coordinate CodingK. Yu, T. Zhang and Y. Gong, NIPS 2009 Improved Local Coordinate Coding Using Local Tangents K. Yu and T. Zhang, ICML 2010Locality-Constrained Linear Coding for Image ClassificationJ. Wang, J. Yang, K. Yu, F. Lv, T. Huang and Y. Gong, CVPR2010 Presented by: Mingyuan Zhou Duke University, ECE September 17, 2010

2. Nonlinear Learning Using Local Coordinate Coding Local Coordinate Coding: Theory

3. Nonlinear Learning Using Local Coordinate Coding Local Coordinate Coding: Practice • Sparse coding: • LLC:

4. Nonlinear Learning Using Local Coordinate Coding Experiments: linear ridge regression based on the sparse codes or LCC

5. Nonlinear Learning Using Local Coordinate Coding Experiments: linear ridge regression

6. Nonlinear Learning Using Local Coordinate Coding Experiments: Handwritten Digit Recognition

7. Nonlinear Learning Using Local Coordinate Coding Experiments: Handwritten Digit Recognition

8. Nonlinear Learning Using Local Coordinate Coding Conclusion

9. Improved Local Coordinate Coding Using Local Tangents Motivation • For smooth but highly nonlinear function, local linear approximation may not necessarily be optimal, which means that many anchor points are needed to achieve accurate approximation. • The improved LCC has better approximation of high dimensional nonlinear functions when the underlying data manifold is locally relatively flat. • It significantly reduces the number of anchor points, leading to reduced computational complexity and improved prediction.

10. Improved Local Coordinate Coding Using Local Tangents VQ, LCC and Improved LCC VQ

11. Improved Local Coordinate Coding Using Local Tangents VQ, LCC and Improved LCC Support: Coding: (Extended LCC) (LCC with local Tangents)

12. Improved Local Coordinate Coding Using Local Tangents Algorithm

13. Improved Local Coordinate Coding Using Local Tangents Experiments The feature dimension is increased from |C| to |C|(1+m) for LCC with local Tangents.

14. Locality-Constrained Linear Coding for Image Classification Introduction • VQ + SPM + Nonlinear SVM • SC + SPM + Linear SVM • LLC + SPM + Linear SVM

15. Locality-Constrained Linear Coding for Image Classification Objective functions • VQ • SC • LLC

16. Locality-Constrained Linear Coding for Image Classification Properties of LLC • Better reconstruction • Local smooth sparsity • Analytical solution • Approximate solution with KNN constraint

17. Locality-Constrained Linear Coding for Image Classification Codebook Optimization

18. Locality-Constrained Linear Coding for Image Classification Experiments

19. Locality-Constrained Linear Coding for Image Classification Experiments