1. Part 3: Image Classification using Sparse Coding: Advanced Topics Kai Yu Dept. of Media Analytics NEC Laboratories America Andrew Ng Computer Science Dept. Stanford University

8. MNIST Experiment: Lambda = 0.0005 05/13/11 Each basis is like a part or direction .

9. MNIST Experiment: Lambda = 0.005 05/13/11 Again, each basis is like a part or direction .

10. MNIST Experiment: Lambda = 0.05 05/13/11 Now, each basis is more like a digit !

11. MNIST Experiment: Lambda = 0.5 05/13/11 Like clustering now!

13. Distribution of coefficients (MNIST) 05/13/11 Neighbor bases tend to get nonzero coefficients

14. Distribution of coefficient (SIFT, Caltech101) 05/13/11 Similar observation here!

18. The image classification setting for analysis Implication : Learning an image classifier is a matter of learning nonlinear functions on patches. Sparse Coding Dense local feature Linear Pooling Linear SVM Function on images Function on patches

19. Illustration: nonlinear l earning via local coding 05/13/11 data points bases locally linear

20. How to learn a nonlinear function? 05/13/11 S tep 1: Learning the dictionary from unlabeled data

21. How to learn a nonlinear function? 05/13/11 S tep 2: Use t he dictionary to encode data

23. L ocal Coordinate Coding (LCC): connect coding to n onlinear f unction l earning 05/13/11 Locality term Function approximation error Coding error If f(x) is (alpha, beta)-Lipschitz smooth Yu et al NIPS-09 T he key message: A good coding scheme should 1. have a small coding error, 2. and also b e sufficiently local

27. The larger dictionary, the higher accuracy, but also the higher computation cost 05/13/11 T he same observation for Caltech-256, PASCAL, ImageNet, … Yu et al NIPS-09 Y ang et al CVPR 09

29. C ompetitive in accuracy, cheap in computation 05/13/11 Wang et al CVPR 10 Sparse coding Significantly better than sparse coding T his is one of the two major algorithms applied by NEC-UIUC team to achieve the No.1 position in ImageNet challenge 2010! Comparable with sparse coding

31. Interpret “BoW + linear classifier” data points cluster centers Piece-wise local constant ( zero-order)

32. Super-vector coding: a simple geometric way to improve BoW (VQ) Zhou et al, ECCV 10 data points cluster centers Piecewise local linear ( first-order) Local tangent

33. Super-vector coding: a simple geometric way to improve BoW (VQ) 05/13/11 Q uantization error Function approximation error If f(x) is beta-Lipschitz smooth, and Local tangent

34. Super-vector coding: learning nonlinear function via a global linear model 05/13/11 Let be the VQ coding of T his is one of the two major algorithms applied by NEC-UIUC team to achieve the No.1 position in PASCAL VOC 2009! Global linear weights to be learned S uper-vector codes of data

40. Learning hierarchical dictionary 05/13/11 Jenatton, Mairal, Obozinski, and Bach, 2010 A node can be active only if its ancestors are active.