Nonlinear Learning Using Local Coordinate Coding K. Yu, T. Zhang and Y. Gong, NIPS 2009 Improved...
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Transcript of Nonlinear Learning Using Local Coordinate Coding K. Yu, T. Zhang and Y. Gong, NIPS 2009 Improved...
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 2010
Locality-Constrained Linear Coding for Image Classification
J. Wang, J. Yang, K. Yu, F. Lv, T. Huang and Y. Gong, CVPR2010
Presented by: Mingyuan ZhouDuke University, ECESeptember 17, 2010
Local Coordinate Coding: TheoryNonlinear Learning Using Local Coordinate Coding
Local Coordinate Coding: Practice
• Sparse coding:
• LLC:
Nonlinear Learning Using Local Coordinate Coding
Experiments: linear ridge regression based on the sparse codes or LCC
Nonlinear Learning Using Local Coordinate Coding
Experiments: linear ridge regression
Nonlinear Learning Using Local Coordinate Coding
Experiments: Handwritten Digit Recognition
Nonlinear Learning Using Local Coordinate Coding
Experiments: Handwritten Digit Recognition
Nonlinear Learning Using Local Coordinate Coding
Conclusion
Nonlinear Learning Using Local Coordinate Coding
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.
Improved Local Coordinate Coding Using Local Tangents
VQ, LCC and Improved LCC
VQ
Improved Local Coordinate Coding Using Local Tangents
VQ, LCC and Improved LCC
Support:
Coding: (Extended LCC)
(LCC with local Tangents)
Improved Local Coordinate Coding Using Local Tangents
Algorithm
Improved Local Coordinate Coding Using Local Tangents
Experiments The feature dimension is increased from |C| to |C|(1+m) for LCC with local Tangents.
Locality-Constrained Linear Coding for Image Classification
Introduction
• VQ + SPM + Nonlinear SVM
• SC + SPM + Linear SVM
• LLC + SPM + Linear SVM
Locality-Constrained Linear Coding for Image Classification
Objective functions
• VQ
• SC
• LLC
Locality-Constrained Linear Coding for Image Classification
Properties of LLC
• Better reconstruction• Local smooth sparsity• Analytical solution
• Approximate solution with KNN constraint
Locality-Constrained Linear Coding for Image Classification
Codebook Optimization
Locality-Constrained Linear Coding for Image Classification
Experiments
Locality-Constrained Linear Coding for Image Classification
Experiments