Joint Weighted Dictionary Learning and Classifier Training for Robust Biometric Recognition

Transcription

1 Joint Weighted Dictionary Learning and Classifier Training for Robust Biometric Recognition Rahman Khorsandi, Ali Taalimi, Mohamed Abdel-Mottaleb, Hairong Qi University of Miami, University of Tennessee, Knoxville {ataalimi,

2 Outline Background Motivation Contribution Exeriment

3 Background Sarse Reresentation-based Classification Training Phase: A.The training dataset: Y c R m n c = {y i,c i {1,!,n c }} Y R m N = {Y c c {1,!,C}} J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma. Robust face recognition via sarse reresentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 31():10 7, Feb

4 Background Sarse Reresentation-based Classification Training Phase: B.Make the dictionary: 1. Fixed D c = [y 1,c,!, y Nc,c ], D = [D 1, D,, D C ] J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma. Robust face recognition via sarse reresentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 31():10 7, Feb

5 Background Sarse Reresentation-based Classification Training Phase: B.Make the dictionary: 1. Fixed:. Learning: D! 1 N i L u (x i, D) L (x, D)! y D x + λ1 x u i x! i,c c i,c i,c 1 i + λ x i,c 5

6 Background Testing Phase Dictionary D from training hase: A. Reconstruct test signal. y Dx * x * t! t t + λ1 x t * 1 + λ x t * δ C (x) = [0 T,!,0 T, x c T,!,0 T ] T c = c y t D c δ c (x t ) l B. Feature extraction. W N h i Wx i + ν W F 6

7 Motivation Sarse Reresentation-based Classification Issues: A. Aly unsuervised dictionary for discriative task. B. Atoms are not required to be uncorrelated. C. Train an indeendent classifier. J.Mairal,F.Bach and J.Ponce. Task-driven dictionary learning. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 34(4): , Aril 01. 7

8 Contribution Learn classifier wrt the current dictionary Task Driven Otimization Bi-level Otimization Minimize correlation between atoms Dictionary that is discriative and reconstructive Weighted Dictionary Learning J.Mairal,F.Bach and J.Ponce. Task-driven dictionary learning. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 34(4): , Aril 01. M. Yang, D. Dai, L. Shen, and L. Van Gool. Latent dictionary learning for sarse reresentation based classification. In Comuter Vision and Pattern Recognition (CVPR),

9 Contribution Task driven dictionary learning Joint estimation of dictionary and classifier: D,W N h i Wx i * (y i,d) + ν W F + λ xi 1 x i,d y i Dx i i Mairal, J., F. Bach, and J. Ponce (01) Task-driven dictionary learning, IEEE Trans. Pattern Anal. Mach. Intell., 34(4),

10 Contribution Weighted Dictionary Learning Correlation between atoms and c-th class: D = γ c = [γ c,1, γ c,,!, γ c, ] T, γ 1,1 γ,1 γ 3,1 γ c,i 0, i {1,!, } = γ γ c,i c,i Y 1 Y Y 3 corr(d i,d j ) (γ c,j γ l,i ) M. Yang, D. Dai, L. Shen, and L. Van Gool. Latent dictionary learning for sarse reresentation based classification. In Comuter Vision and Pattern Recognition (CVPR),

11 Contribution Weighted Dictionary Learning D,γ c,x C +λ 1 X c 1 c=1 Y c Ddiag(γ c )X c F Reconstruct data as: C +λ γ c,j c=1 l c j i (d j T d i ) γ l,i Y c Ddiag(γ c )X c γ c,i 0 and γ c,i = γ l,i, c,l M. Yang, D. Dai, L. Shen, and L. Van Gool. Latent dictionary learning for sarse reresentation based classification. In Comuter Vision and Pattern Recognition (CVPR),

12 Contribution D,W N h i Wx i * (y i, D) + ν W F Task Driven D,Γ,X C +λ 1 X c 1 c=1 Y c Ddiag(γ c )X c F C +λ γ c,j c=1 l c γ c,i 0 and j i (d j T d i ) γ l,i γ c,i = γ l,i, c,l Weighted Dictionary Learning 1

13 Otimization First Ste Constant Γ γ c solve for D and X c c 13

14 Otimization First Ste Constant γ c 1 X c Y Ddiag(γ )X + λ X c c c F c 1 solve for D c and X c D λ C c=1 C Y Ddiag(γ )X + c c c F c=1 l c j i γ c,j (d j T d i ) γ l,i L. Rosasco, A. Verri, M. Santoro, S. Mosci, and S. Villa. Iterative rojection methods for structured sarsity regularization M. Yang, D. Dai, L. Shen, and L. Van Gool. Latent dictionary learning for sarse reresentation based classification. In Comuter Vision and Pattern Recognition (CVPR),

15 Otimization Second Ste Constant solve for D and X γ c γ c Y c Ddiag(γ c )X c F λ γ (d! d ) c,i j i j i + l c γ l,j Third Ste Constant X solve for W W N h i Wx i + ν W F Z. Jiang, Z. Lin, and L. S. Davis. Label consistent k-svd: learning a discriative dictionary for recognition. Pattern Analysis and Machine Intelligence, 013. L. Rosasco, A. Verri, M. Santoro, S. Mosci, and S. Villa. Iterative rojection methods for structured sarsity regularization Mairal, J., F. Bach, and J. Ponce (01) Task-driven dictionary learning, IEEE Trans. Pattern Anal. Mach. Intell., 34(4),

16 D, γ c Testing hase From Training: x t,c Y t Ddiag(γ c )x t,c F +λ1 x t,c 1 Weighted +λ γ c,j l c j i (d j T d i ) γ l,i Dictionary Learning E t,c = y t Ddiag(γ c )x t,c +η h c Wx t,c 16

17 Quantitative Comarison UND data set A. 35 male and 169 female subjects. 17

18 Quantitative Comarison WVU data set 5 atoms er subject. HoG feature. EAR RECOGNITION RATES ON WVU DATABASE. EAR RECOGNITION RATES UNDER DIFFERENT RATIOS OF RANDOM CORRUPTION. 18