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Fcv learn yu Fcv learn yu Presentation Transcript

  • Sparse Coding and Its Extensions for Visual Recognition Kai Yu M edia Analytics Department NEC Labs America, C upertino, CA
  • V isual Recognition is HOT in Computer Vision 12/30/11 C altech 101 PASCAL VOC 80 Million Tiny Images I mageNet
  • T he pipeline of machine visual perception 12/30/11 M ost Efforts in Machine Learning Low-level sensing Pre-processing Feature extract. Feature selection Inference: prediction, recognition
    • M ost c ritical for accuracy
    • A ccount for most of the computation
    • Most time-consuming in development cycle
    • O ften hand-craft in practice
  • Computer vision features SIFT Spin image HoG RIFT S lide Credit: Andrew Ng GLOH
  • L earning everything from data 12/30/11 Machine Learning Low-level sensing Pre-processing Feature extract. Feature selection Inference: prediction, recognition M achine L earning
  • BoW + SPM Kernel 12/30/11
    • Combining multiple features, this method had been the state-of-the-art on Caltech-101, PASCAL, 15 Scene Categories, …
    Figure credit: Fei-Fei Li, Svetlana Lazebnik Bag-of-visual-words representation (BoW) based on vector quantization (VQ) Spatial pyramid matching (SPM) kernel
  • W inning Method in PASCAL VOC before 2009 12/30/11 M ultiple Feature Sampling Methods Multiple Visual Descriptors VQ C oding , H istogram, SPM N onlinear SVM
  • Convolution Neural Networks
    • T he architectures of some successful methods are not so much different from CNNs
    Conv. Filtering Pooling Conv. Filtering Pooling
  • BoW+SPM: the same architecture
    • Observations:
    • Nonlinear SVM is not scalable
    • VQ coding may be too coarse
    • Average pooling is not optimal
    • Why not learn the whole thing?
    e.g, SIFT, HOG VQ Coding Average Pooling (obtain histogram) Nonlinear SVM Local Gradients Pooling
  • D evelop better methods Better Coding Better Pooling Scalable Linear Classifier B etter Coding B etter Pooling
  • S parse Coding 12/30/11 Sparse coding (Olshausen & Field,1996). Originally developed to explain early visual processing in the brain (edge detection). T raining: given a set of random patches x, learning a dictionary of bases [Φ 1, Φ 2, …] Coding: for data vector x, solve LASSO to find the sparse coefficient vector a
  • Sparse Coding E xample Natural Images Learned bases (  1 , …,  64 ): “Edges” x  0.8 *  36 + 0.3 *  42 + 0.5 *  63 [a 1 , …, a 64 ] = [ 0, 0, …, 0, 0.8 , 0, …, 0, 0.3 , 0, …, 0, 0.5 , 0 ] (feature representation) Test example Compact & easily interpretable Slide credit: Andrew Ng  0.8 * + 0.3 * + 0.5 *
  • S elf-taught Learning Testing: What is this? Motorcycles Not motorcycles [Raina, Lee, Battle, Packer & Ng, ICML 07] Testing: What is this ? Slide credit: Andrew Ng Unlabeled images …
  • Classification R esult on Caltech 101 12/30/11 64% SIFT VQ + N onlinear SVM 50% Pixel S parse Coding + Linear SVM 9K images, 101 classes
  • e.g, SIFT, HOG S parse Coding on SIFT [Y ang, Yu, Gong & Huang , CVPR09] S parse Coding M ax Pooling Scalable Linear Classifier Local Gradients Pooling
  • 12/30/11 64% SIFT VQ + N onlinear SVM 73% SIFT S parse Coding + Linear SVM C altech-101 S parse Coding on SIFT [Y ang, Yu, Gong & Huang , CVPR09]
  • W hat we have learned?
    • S parse coding is a useful stuff (why?)
    • H ierarchical architecture is needed
    e.g, SIFT, HOG S parse Coding M ax Pooling Scalable Linear Classifier Local Gradients Pooling
  • MNIST E xperiments 12/30/11 Error: 4.54%
    • When SC achieves the best classification accuracy, the learned bases are like digits – each basis has a clear local class association.
    Error: 3.75% Error: 2.64%
  • Distribution of coefficient (SIFT, Caltech101) 12/30/11 Neighbor bases tend to get nonzero coefficients
  • 12/30/11
    • I nterpretation 2
    • Geometr y of data manifold
    • Each basis an “ anchor point ”
    • Sparsity is induced by locality : each datum is a linear combination of neighbor anchors.
    • I nterpretation 1
    • Discover subspaces
    • Each basis is a “ direction ”
    • Sparsity : each datum is a linear combination of only several bases.
    • Related to topic model
  • A F unction Approximation View to Coding 12/30/11
    • S etting : f(x) is a nonlinear feature extraction function on image patches x
    • Coding : nonlinear mapping
    • x  a
    • typically, a is high-dim & sparse
    • Nonlinear Learning :
    • f(x) = <w, a>
    A coding scheme is good if it helps learning f(x)
  • A F unction Approximation View to Coding – The General Formulation 12/30/11 F unction Approx. Error ≤ A n unsupervised learning objective
  • Local Coordinate Coding (LCC) 12/30/11
    • D ictionary Learning: k-means (or hierarchical k -means)
    • C oding for x, to obtain its sparse representation a
      • Step 1 – ensure locality : find the K nearest bases
      • Step 2 – ensure low coding error :
    Yu, Zhang & Gong, NIPS 09 W ang, Yang, Yu, Lv, Huang CVPR 10
  • Super-Vector Coding (SVC) 12/30/11
    • D ictionary Learning: k-means (or hierarchical k -means)
    • C oding for x, to obtain its sparse representation a
      • Step 1 – find the nearest bas i s of x, obtain its VQ coding
      • e.g. [0, 0, 1, 0, …]
      • Step 2 – form super vector coding:
      • e.g. [0, 0, 1, 0, …, 0, 0, (x-m 3 ), 0 ,… ]
    Zhou, Yu, Zhang, and Huang, ECCV 10 Zero-order Local tangent
  • F unction Approximation based on LCC 12/30/11 data points bases Yu, Zhang, Gong, NIPS 10 locally linear
  • Function Approximation based on SVC Zhou, Yu, Zhang, and Huang, ECCV 10 data points cluster centers Piecewise local linear ( first-order) Local tangent
  • PASCAL VOC C hallenge 2009 12/30/11 N o.1 for 18 of 20 categories W e used only HOG feature on gray images Ours Best of Other Teams Difference Classes
  • I mageNet Challenge 2010 12/30/11 ~40% VQ + I ntersection Kernel 64%~73% Various Coding Methods + Linear SVM 1.4 million images, 1000 classes, top5 hit rate 50% Classification accuracy
  • H ierarchical sparse coding Yu, Lin, & Lafferty, CVPR 11 Conv. Filtering Pooling Conv. Filtering Pooling L earning from unlabeled data
  • A two-layer sparse coding formulation 12/30/11
  • MNIST Results -- classification  HSC vs. CNN: HSC provide even better performance than CNN  more amazingly, HSC learns features in unsupervised manner!
  • MNIST results -- effect of hierarchical learning C omparing the Fisher score of HSC and SC  Discriminative power: is significantly improved by HSC although HSC is unsupervised coding
  • MNIST results -- learned codebook One dimension in the second layer: invariance to translation, rotation, and deformation
  • Caltech101 results -- classification  Learned descriptor: performs slightly better than SIFT + SC
  • Caltech101 results -- learned codebook  First layer bases: very much like edge detectors.
  • Conclusion and Future Work
    • “ function approximation ” view to derive novel sparse coding methods.
    • Locality – one way to achieve sparsity and it’s really useful. But we need deeper understanding of the feature learning methods
    • Interesting directions
      • Hierarchical coding – Deep Learning (many papers now!)
      • Faster methods for sparse coding (e.g. from LeCun’s group)
      • Learning features from a richer structure of data, e.g., video (learning invariance to out plane rotation)
  • References 12/30/11
    • L earning Image Representations from Pixel Level via Hierarchical Sparse Coding,
    • K ai Yu, Yuanqing Lin, John Lafferty. CVPR 2011
    • Large-scale Image Classification: Fast Feature Extraction and SVM Training,
    • Y uanqing Lin, Fengjun Lv, Liangliang Cao, Shenghuo Zhu, Ming Yang, Timothee Cour, Thomas Huang, Kai Yu
    • in CVPR 2011
    • ECCV 2010 Tutorial, Kai Yu, Andrew Ng (with links to some source codes)
    • Deep Coding Networks,
    • Yuanqing Lin, Tong Zhang, Shenghuo Zhu, Kai Yu. In NIPS 2010 .
    • Image Classification using Super-Vector Coding of Local Image Descriptors,
    • Xi Zhou, Kai Yu, Tong Zhang, and Thomas Huang. In ECCV 2010 .
    • Efficient Highly Over-Complete Sparse Coding using a Mixture Model,
    • Jianchao Yang, Kai Yu, and Thomas Huang. In ECCV 2010 .
    • Improved Local Coordinate Coding using Local Tangents,
    • Kai Yu and Tong Zhang. In ICML 2010 .
    • Supervised translation-invariant sparse coding,
    • Jianchao Yang, Kai Yu, and Thomas Huang, In CVPR 2010
    • Learning locality-constrained linear coding for image classification,
    • Jingjun Wang, Jianchao Yang, Kai Yu, Fengjun Lv, Thomas Huang. In CVPR 2010 .
    • Nonlinear learning using local coordinate coding,
    • Kai Yu, Tong Zhang, and Yihong Gong. In NIPS 2009 .
    • Linear spatial pyramid matching using sparse coding for image classification,
    • Jianchao Yang, Kai Yu, Yihong Gong, and Thomas Huang. In CVPR 2009 .