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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
Outline of Part 3 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Outline of Part 3 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Intuition: why sparse coding helps classification? 05/13/11 ,[object Object],[object Object],[object Object],Figure from  http://www.dtreg.com/svm.htm
A “topic model” view to sparse coding 05/13/11 ,[object Object],[object Object],[object Object],B oth f igures adapted from CVPR10 tutorial by F. Bach, J. Mairal, J. Ponce and G. Sapiro Basis 1 Basis 2
A geometric view to sparse coding 05/13/11 Data manifold ,[object Object],[object Object],[object Object],Basis Data
MNIST Experiment: Classification using SC 05/13/11 ,[object Object],[object Object],[object Object],Try different values
MNIST Experiment: Lambda = 0.0005 05/13/11 Each basis is like a  part  or  direction .
MNIST Experiment: Lambda = 0.005 05/13/11 Again, each basis is like a  part  or  direction .
MNIST Experiment: Lambda = 0.05 05/13/11 Now, each basis is more like a  digit  !
MNIST Experiment: Lambda = 0.5 05/13/11 Like clustering now!
Geometric view of sparse coding 05/13/11 Error: 4.54% ,[object Object],[object Object],Error: 3.75% Error: 2.64%
Distribution of coefficients (MNIST)  05/13/11 Neighbor bases tend to get nonzero coefficients
Distribution of coefficient (SIFT, Caltech101) 05/13/11 Similar observation here!
Recap: two different views to sparse coding 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Outline of Part 3 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Key theoretical question 05/13/11 ,[object Object]
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
Illustration:  nonlinear l earning  via local coding 05/13/11 data points bases locally linear
How to learn a nonlinear function? 05/13/11 S tep 1: Learning the  dictionary  from unlabeled data
How to learn a nonlinear function? 05/13/11 S tep 2: Use  t he dictionary to encode data
How to learn a nonlinear function? ,[object Object],05/13/11 Sparse codes of data S tep 3:  Estimate parameters  Global linear weights to be learned
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
Outline of Part 3 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Application of LCC theory 05/13/11 ,[object Object],[object Object],Wang  e t al, CVPR 10 Zhou et al, ECCV 10
Application of LCC theory 05/13/11 ,[object Object],[object Object]
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
L ocality-constrained linear coding  a fast implementation of LCC 05/13/11 ,[object Object],[object Object],[object Object],[object Object],Wang et al, CVPR 10
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
Application of the LCC theory 05/13/11 ,[object Object],[object Object]
Interpret “BoW + linear classifier” data points cluster centers Piece-wise local constant ( zero-order)
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
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
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
Summary of Geometric Coding Methods Super-vector Coding ,[object Object],[object Object],[object Object],[object Object],Vector Quantization (BoW)  (Fast) Local Coordinate Coding
Things not covered here 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Outline of Part 3 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Fast approximation of sparse coding via neural networks 05/13/11 Gregor & LeCun, ICML-10 ,[object Object],[object Object],[object Object]
Group sparse coding 05/13/11 ,[object Object],[object Object],[object Object],Bengio et al, NIPS 09
Learning hierarchical dictionary 05/13/11 Jenatton, Mairal, Obozinski, and Bach, 2010 A node can be active only if its ancestors are active.
Reference 05/13/11 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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ECCV2010: feature learning for image classification, part 3

  • 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
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 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!
  • 12.
  • 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!
  • 15.
  • 16.
  • 17.
  • 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
  • 22.
  • 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
  • 24.
  • 25.
  • 26.
  • 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
  • 28.
  • 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
  • 30.
  • 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
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40. Learning hierarchical dictionary 05/13/11 Jenatton, Mairal, Obozinski, and Bach, 2010 A node can be active only if its ancestors are active.
  • 41.

Hinweis der Redaktion

  1. Let’s further check what’s happening when best classification performance is achieved.