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**Sparse Coding and Its Extensions for Visual Recognition**

Kai Yu Media Analytics Department NEC Labs America, Cupertino, CA

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**Visual Recognition is HOT in Computer Vision**

80 Million Tiny Images Caltech 101 ImageNet PASCAL VOC 3/27/2017

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**The pipeline of machine visual perception**

Most Efforts in Machine Learning Low-level sensing Pre-processing Feature extract. Feature selection Inference: prediction, recognition Most critical for accuracy Account for most of the computation Most time-consuming in development cycle Often hand-craft in practice 3/27/2017

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**Computer vision features**

SIFT Spin image HoG RIFT GLOH Slide Credit: Andrew Ng

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**Learning everything from data**

Machine Learning Low-level sensing Pre-processing Feature extract. Feature selection Inference: prediction, recognition Machine Learning 3/27/2017

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BoW + SPM Kernel Bag-of-visual-words representation (BoW) based on vector quantization (VQ) Spatial pyramid matching (SPM) kernel Combining multiple features, this method had been the state-of-the-art on Caltech-101, PASCAL, 15 Scene Categories, … 3/27/2017 Figure credit: Fei-Fei Li, Svetlana Lazebnik

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**Winning Method in PASCAL VOC before 2009**

VQ Coding, Histogram, SPM Multiple Feature Sampling Methods Multiple Visual Descriptors Nonlinear SVM 3/27/2017

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**Convolution Neural Networks**

Conv. Filtering Pooling Conv. Filtering Pooling The architectures of some successful methods are not so much different from CNNs

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**BoW+SPM: the same architecture**

e.g, SIFT, HOG VQ Coding Average Pooling (obtain histogram) Nonlinear SVM Local Gradients Pooling Observations: Nonlinear SVM is not scalable VQ coding may be too coarse Average pooling is not optimal Why not learn the whole thing?

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**Develop better methods**

Better Coding Better Pooling Scalable Linear Classifier

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Sparse Coding Sparse coding (Olshausen & Field,1996). Originally developed to explain early visual processing in the brain (edge detection). Training: given a set of random patches x, learning a dictionary of bases [Φ1, Φ2, …] Coding: for data vector x, solve LASSO to find the sparse coefficient vector a 3/27/2017

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**Sparse Coding Example x » 0.8 * f36 + 0.3 * f42 + 0.5 * f63**

Natural Images Learned bases (f1 , …, f64): “Edges” Test example » 0.8 * * * x » 0.8 * f * f * f63 [a1, …, a64] = [0, 0, …, 0, 0.8, 0, …, 0, 0.3, 0, …, 0, 0.5, 0] (feature representation) Compact & easily interpretable Slide credit: Andrew Ng

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**… Self-taught Learning Motorcycles Not motorcycles Unlabeled images**

[Raina, Lee, Battle, Packer & Ng, ICML 07] Motorcycles Not motorcycles Unlabeled images … Testing: What is this? Testing: What is this? Slide credit: Andrew Ng

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**Classification Result on Caltech 101**

9K images, 101 classes 64% SIFT VQ + Nonlinear SVM 50% Pixel Sparse Coding + Linear SVM 3/27/2017

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**Scalable Linear Classifier**

Sparse Coding on SIFT [Yang, Yu, Gong & Huang, CVPR09] Sparse Coding Max Pooling Scalable Linear Classifier Local Gradients Pooling e.g, SIFT, HOG

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**64% 73% Sparse Coding on SIFT Caltech-101 SIFT VQ + Nonlinear SVM**

[Yang, Yu, Gong & Huang, CVPR09] Caltech-101 64% SIFT VQ + Nonlinear SVM 73% SIFT Sparse Coding + Linear SVM 3/27/2017

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**Scalable Linear Classifier**

What we have learned? Sparse Coding Max Pooling Scalable Linear Classifier Local Gradients Pooling e.g, SIFT, HOG Sparse coding is a useful stuff (why?) Hierarchical architecture is needed

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MNIST Experiments Error: 4.54% Error: 3.75% Error: 2.64% When SC achieves the best classification accuracy, the learned bases are like digits – each basis has a clear local class association. 3/27/2017

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**Distribution of coefficient (SIFT, Caltech101)**

Neighbor bases tend to get nonzero coefficients 3/27/2017

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**Geometry of data manifold**

Interpretation 1 Discover subspaces Each basis is a “direction” Sparsity: each datum is a linear combination of only several bases. Related to topic model Interpretation 2 Geometry of data manifold Each basis an “anchor point” Sparsity is induced by locality: each datum is a linear combination of neighbor anchors. 3/27/2017

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**A Function Approximation View to Coding**

Setting: 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) 3/27/2017

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**A Function Approximation View to Coding – The General Formulation**

Function Approx. Error An unsupervised learning objective ≤ 3/27/2017

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**Local Coordinate Coding (LCC)**

Yu, Zhang & Gong, NIPS 09 Wang, Yang, Yu, Lv, Huang CVPR 10 Dictionary Learning: k-means (or hierarchical k-means) Coding for x, to obtain its sparse representation a Step 1 – ensure locality: find the K nearest bases Step 2 – ensure low coding error: 3/27/2017

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**Super-Vector Coding (SVC)**

Zhou, Yu, Zhang, and Huang, ECCV 10 Dictionary Learning: k-means (or hierarchical k-means) Coding for x, to obtain its sparse representation a Step 1 – find the nearest basis 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-m3），0，…] Zero-order Local tangent 3/27/2017

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**Function Approximation based on LCC**

Yu, Zhang, Gong, NIPS 10 locally linear data points bases 3/27/2017

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**Function Approximation based on SVC**

Zhou, Yu, Zhang, and Huang, ECCV 10 Piecewise local linear (first-order) Local tangent data points cluster centers

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**PASCAL VOC Challenge 2009 No.1 for 18 of 20 categories**

Ours Best of Other Teams Difference Classes No.1 for 18 of 20 categories We used only HOG feature on gray images 3/27/2017

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**1.4 million images, 1000 classes,**

ImageNet Challenge 2010 1.4 million images, 1000 classes, top5 hit rate ~40% VQ + Intersection Kernel 64%~73% Various Coding Methods + Linear SVM 50% Classification accuracy 3/27/2017

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**Hierarchical sparse coding**

Yu, Lin, & Lafferty, CVPR 11 Learning from unlabeled data Conv. Filtering Pooling Conv. Filtering Pooling

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**A two-layer sparse coding formulation**

3/27/2017

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**MNIST Results -- classification**

HSC vs. CNN: HSC provide even better performance than CNN more amazingly, HSC learns features in unsupervised manner!

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**MNIST results -- effect of hierarchical learning**

Comparing the Fisher score of HSC and SC Discriminative power: is significantly improved by HSC although HSC is unsupervised coding

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**MNIST results -- learned codebook**

One dimension in the second layer: invariance to translation, rotation, and deformation

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**Caltech101 results -- classification**

Learned descriptor: performs slightly better than SIFT + SC

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**Caltech101 results -- learned codebook**

First layer bases: very much like edge detectors.

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**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)

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References Learning Image Representations from Pixel Level via Hierarchical Sparse Coding, Kai Yu, Yuanqing Lin, John Lafferty. CVPR 2011 Large-scale Image Classification: Fast Feature Extraction and SVM Training, Yuanqing 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. 3/27/2017

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