ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Random Feature Selection for Robust Face Recognition Allen Y. Yang <yang@eecs.berkeley.edu> Department of EECS, UC Berkeley with Shankar Sastry, Yi Ma, & John Wright HSN MIT Review, Sep 24, 2007 Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Next Generation Sensor Networks Transition from dedicated sensor networks to general-purpose sensor networks. 1 Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Next Generation Sensor Networks Transition from dedicated sensor networks to general-purpose sensor networks. 1 Similar revolutions in IT industry: 2 Computer: Services: Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Advances in Sensor Networks Proliferation 1 (a) Ubiquitous (b) Mobile (c) Personal Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Advances in Sensor Networks Proliferation 1 (a) Ubiquitous (b) Mobile (c) Personal More powerful processing units 2 Intel XScale 600MHz CPU Memory: 16 MB ROM, 64 MB RAM Resolution: 1280 × 1024 up to 15 fps Integrated microphone, infrared, motion sensors. IEEE 802.15.4 protocal, 250 kbps. Figure: Next generation Berkeley wireless camera mote. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions On-Demand Surveillance Distributed recognition system: 1 Multi-tasking. Adaptive to environments. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions On-Demand Surveillance Distributed recognition system: 1 Multi-tasking. Adaptive to environments. Adaptive feature selection is critical for on-demand surveillance. 2 Thermometer, infrared: simple thresholding. Face IDs: Action: spatial-temporal features in video sequences. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions On-Demand Surveillance Distributed recognition system: 1 Multi-tasking. Adaptive to environments. Adaptive feature selection is critical for on-demand surveillance. 2 Thermometer, infrared: simple thresholding. Face IDs: Action: spatial-temporal features in video sequences. Sensor-server network 3 On-demand surveillance and band-limited channels present a conundrum. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Contributions Qualification for feature selection Data independent. Application independent. Fast to generate and compute. Accurate in preserving true data structures. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Contributions Qualification for feature selection Data independent. Application independent. Fast to generate and compute. Accurate in preserving true data structures. Contributions New framework for object/face recognition via compressed sensing. 1 Classification is encoded in a (global) sparse representation. 2 Random projection as universal dimensionality redunction. 3 Efficient solution via ℓ 1 -minimization outperforms classical algorithms. 4 Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Representation using Linear Models Representation of samples in vector form y ∈ R D . 1 Figure: Stacking of 2-D image. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Representation using Linear Models Representation of samples in vector form y ∈ R D . 1 Figure: Stacking of 2-D image. Recognition (supervised learning) 2 Training: For K classes, collect samples { v 1 , 1 , · · · , v 1 , n 1 } , · · · , { v K , 1 , · · · , v K , nK } . Test: Present a new y , solve for label( y ) ∈ [1 , 2 , · · · , K ]. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Representation using Linear Models Representation of samples in vector form y ∈ R D . 1 Figure: Stacking of 2-D image. Recognition (supervised learning) 2 Training: For K classes, collect samples { v 1 , 1 , · · · , v 1 , n 1 } , · · · , { v K , 1 , · · · , v K , nK } . Test: Present a new y , solve for label( y ) ∈ [1 , 2 , · · · , K ]. Subspace model for face recognition: [Belhumeur et al. 1997, Basri & Jocobs 2003] 3 y = α i , 1 v i , 1 + α i , 2 v i , 2 + · · · + α i , n 1 v i , n i , = A i α i , where A i = [ v i , 1 , v i , 2 , · · · , v i , n i ]. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Recognition via Sparse Representation The label of y is unknown: 1 α 1 α 2 , = [ A 1 , A 2 , · · · , A K ] . y . . α K = A x 0 . Over-determined system: A ∈ R D × n , where D ≫ n = n 1 + · · · + n K . Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Recognition via Sparse Representation The label of y is unknown: 1 α 1 α 2 , = [ A 1 , A 2 , · · · , A K ] . y . . α K = A x 0 . Over-determined system: A ∈ R D × n , where D ≫ n = n 1 + · · · + n K . x 0 encodes membership of y : If y belongs to Subject 1, 2 α 1 0 0 ∈ R n . x 0 = . . . 0 That is, y should be only represented using the same subject! Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Recognition via Sparse Representation The label of y is unknown: 1 α 1 α 2 , = [ A 1 , A 2 , · · · , A K ] . y . . α K = A x 0 . Over-determined system: A ∈ R D × n , where D ≫ n = n 1 + · · · + n K . x 0 encodes membership of y : If y belongs to Subject 1, 2 α 1 0 0 ∈ R n . x 0 = . . . 0 That is, y should be only represented using the same subject! If we recover sparse x 0 , recognition is solved! Not so fast!! Directly solving A is expensive: D > 7 × 10 4 for a 320 × 240 grayscale image. 1 x 0 is sparse: K terms non-zero. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Dimensionality Redunction Dimensionality redunction 1 Construct linear projection R ∈ R d × D , d is the feature dimension. y . = R y = RA x 0 = ˜ ˜ A x 0 . ˜ A ∈ R d × n , but x 0 is unchanged. Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Dimensionality Redunction Dimensionality redunction 1 Construct linear projection R ∈ R d × D , d is the feature dimension. y . = R y = RA x 0 = ˜ ˜ A x 0 . ˜ A ∈ R d × n , but x 0 is unchanged. Holistic features 2 Eigenfaces [Turk & Pentland 1991] Fisherfaces [Belhumeur et al. 1997] Laplacianfaces [He et al. 2005] Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
ℓ 1 -Minimization Motivation Problem Formulation Classification Experiments Future Directions Dimensionality Redunction Dimensionality redunction 1 Construct linear projection R ∈ R d × D , d is the feature dimension. y . = R y = RA x 0 = ˜ ˜ A x 0 . ˜ A ∈ R d × n , but x 0 is unchanged. Holistic features 2 Eigenfaces [Turk & Pentland 1991] Fisherfaces [Belhumeur et al. 1997] Laplacianfaces [He et al. 2005] Partial features 3 Allen Y. Yang <yang@eecs.berkeley.edu> Random Feature Selection for Robust Face Recognition
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