Supervised Translation-Invariant
Sparse Coding
[Jianchao Yang, Kai Yu, Thomas Huang]
讲解人: 崔 振
2010.9.17
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
Jianchao Yang

Image Formation & Processsing Group (IFP), University
of Illinois at Urbana-Champaign (UIUC)

Ph.D. Candidate (06-Present, ECE, UIUC) ; Ph.D.
Adviser: Prof. Thomas S. Huang
B.Eng (02-06, EEIS, USTC)
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Publication（第一作者）
 CVPR：4篇，2篇oral
 TIP：2篇
 ECCV10，1篇
 ICIP,1篇

Homepage: http://www.ifp.illinois.edu/~jyang29/
jyang29 @ifp.uiuc.edu
Kai Yu

Machine Learning researcher and the Head of Media
Analytics Department at NEC Laboratories America. Inc..

Ph.D. Computer Science, University of Munich,Germany,
January 2001 – July 2004.
B.Sc and M.Sc, Nanjing University.
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Research Interests
 Areas: machine learning, data mining, information
retrieval, computer vision
CVPR(4),ECCV(4+),ICML(8+),NIPS(10+),…

http://www.dbs.informatik.uni-muenchen.de/~yu_k/

Thomas Huang

Beckman Institute Image Formation and Processing
and Artificial Intelligence groups.
William L. Everitt Distinguished Professor in the U of I
Department of Electrical and Computer Engineering
and the Coordinated Science Lab (CSL);

Sc.D. from MIT in 1963

computer vision, image compression and
enhancement, pattern recognition, and multimodal
signal processing.

http://www.beckman.illinois.edu/directory/t-huang1
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提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
文章信息


文章出处
 CVPR10（oral）
相关文章
 Yang et al. Linear spatial pyramid matching using
sparse coding for image classification. CVPR’09.
Abstract

In this paper, we propose a novel supervised hierarchical
sparse coding model based on local image descriptors for
classification tasks. The supervised dictionary training is
performed via back-projection, by minimizing the training error
of classifying the image level features, which are extracted by
max pooling over the sparse codes within a spatial pyramid.
Such a max pooling procedure across multiple spatial scales
offer the model translation invariant properties, similar to the
Convolutional Neural Network (CNN). Experiments show that
our supervised dictionary improves the performance of the
proposed model significantly over the unsupervised dictionary,
leading to state-of-the-art performance on diverse image
databases. Further more, our supervised model targets
learning linear features, implying its great potential in handling
large scale datasets in real applications.
摘要



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针对分类任务，提出了一种新颖的基于局部图像描述子的
监督分级稀疏编码模型。
通过back-projection方法，以最小化在图像层级特征
(image level features)的分类误差训练监督词典。其中图
像层级特征是以空间金字塔为结构max pooling稀疏编码。
在多种空间尺度下max pooling方法具有平移不变的特性，
如同CNN(Convolutional Neural Network)一样。
实验证明，与无监督词典相比，监督词典明显地改善了模
型的性能，并且在多个图像数据库拥有最好的表现。
另外，监督模型目标是学习线性特征，它蕴含了一个巨大
潜能-实时地处理大规模数据库。
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
拟解决的问题

Image classification
 To find a generic feature representation
 Interested in linear prediction model
Sparse Coding for Image Classification
Sparse Coding
Unsupervised
Supervised
Sparse coding on holistic image
-Linear model assumption
-Sensitive to image misalignment
-Limited applications
D. Bradley et al. ‘08
J. Wright et al. ’09
A. Wagner et al.’09
etc
D. Bradley et al. ‘08
J. Marialet al. ’08
Q. Zhang. CVPR10
etc
Sparse coding on local
descriptors
-Break linear model assumption
for the image space
-Robust to image misalignment
-Applicableto generic image
classification
R. Rainaet al. ’07
J. Yang et al. ’09
J. Yang et al. ’10
etc
？
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
本文的方法
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
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框架
相关知识
本文模型
求解方法
框架
Descriptor extraction
Bag of coordinated
Local descriptors
nonlinear coding
Yang. CVPR09
High-dimensional
sparse codes
feature pooling
Image
representation
classification
It must be a cool
Cat!
J. Yang et al. Linear spatial pyramid matching using sparse coding for image classification. CVPR’09.
已有方法


Histogram-based SPM feature
 Step 1: local descriptor extraction
 Step 2: vector quantization (e.g.k-means)
 Step 3: hierarchical average pooling
 Step 4: nonlinear SVM
The framework of ScSPM （CVPR09）
 Step 1: local descriptor extraction
 Step 2: sparse coding (无监督词典)
 Step 3: hierarchical max pooling
 Step 4: linear SVM
相关知识(1)

Sparse coding
Xnxm=(X1,X2,…,Xm)
Bnxk：词典

Max pooling
Zkxm：稀疏系数
相关知识(2)
S: 尺度（层次）
U: 串接
分级融合
Model（1）
Xk：表示第k个图像
目标函数
+ SVM
多层max pooling
Model（2）-目标函数
监督
Optimization over B: back propagation!
求解方法（1）
No analytical
link
Linear
prediction
Squared
hinge
Only cares about
loss model
function
the pooled
maximum values
求解方法（2）

Solution: use implicit differentiation
Setting the gradients at
zero coefficients to be zero,
a lot of computations can
be saved!
D. M. Bradley et al. Differentiable sparse coding. NIPS 2008.
Training convergence
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Initialization is important: B is trained in unsupervised
manner.
Convergence
Example dictionary
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Example dictionary: CMU PIE
Unsupervised
Supervised
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
Experiment
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Classification tasks
 Face recognition: CMU PIE, and CMU Multi-PIE
 Handwritten digit recognition: MNIST
 Gender Recognition: FRGC 2.0
Image local descriptors: raw image patches
Prediction model: one-vs-all linear SVM with squared hinge loss
function.
Stochastic optimization: typically converges in 10 iterations,
gradient descent.
Experiment
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Parameter settings
学习率：
Experiment –Face Recognition (1)
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CMU PIE:
 41368 images of 68 people, each under 13 poses, 43
different illumination conditions with 4 different
expressions.
 A subset of five near frontal views are used including
all expressions and illuminations.
Experiment –Face Recognition (1)
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USC: unsupervised sparse coding model.
SSC: supervised sparse coding model.
Improvements: shows the improvements of SSC over
USC.
Classification error(%) on CMU PIE
Experiment –Face Recognition (2)

CMU Multi-PIE:
 contains 337 subjects across simultaneous variations
in pose, expression and illumination.
 A subset containing near frontal view face images are
used as training and testing.
Experiment –Face Recognition (2)
Face recognition error(%) on Multi-PIE
[SR] A. Wagner et al. Towards a practical face recognition system:
robust registration and illumination by sparse representation. CVPR’09.
Experiment – Handwritten Digit Recognition

MNIST: consists of 70,000 handwritten digits, aligned to
the center. 60,000 of them are modeled as training, and
the rest 10,000 as testing.
Experiment – Gender Recognition

FRGC 2.0
 contains 568 individuals, totally 14714 face images
under various lighting conditions and backgrounds.
 11700 face images of 451 individuals are used as
training, and the remaining 3014 images of 114
persons are used as testing.
Experiment – Gender Recognition
提纲
•作者信息
•文章信息
•拟解决的问题
•本文的方法
•实验
•结论
Conclusion


A supervised translation-invariant sparse coding model for image
classification
 A generic image representation.
 The max pooling feature is translation-invariant.
 Sparse coding on local descriptors is promising compared to
sparse coding on holistic image.
 Supervised sparse coding improves the performance significantly.
Next steps:
 Connections with hierarchical models in deep belief networks
should be investigated.
 More theoretical analysis for pooling functions are needed.
 Deep hierarchical models based on sparse coding should be
studied.
参考文献
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Jianchao Yang, Kai Yu, Thomas Huang,Supervised TranslationInvariant Sparse Coding. CVPR10.
J. Yang et al. Translation-Invariant Sparse Coding. CVPR10(talk).
J. Yang et al. Linear spatial pyramid matching using sparse coding
for image classification. CVPR’09.