Transcript Nonlinear Learning Using Local Coordinate Coding K. Yu, T. Zhang

Nonlinear Learning Using Local Coordinate Coding
K. 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 Zhou
Duke University, ECE
September 17, 2010
Nonlinear Learning Using Local Coordinate Coding
Local Coordinate Coding: Theory
Nonlinear 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
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