Kernel orthogonal and uncorrelated neighborhood preservation discriminant embedding algorithm

Transcript

1 32 7 Vol Journal of Harbn Engneerng Unversty Jul 2011 do /j ssn Yale PIE TE2 TP Kernel orthogonal and uncorrelated neghborhood preservaton dscrmnant embeddng algorthm LIU Guanqun WANG Qngjun ZHANG Rubo PAN Hawe College of Computer Scence and Technology Harbn Engneerng Unversty Harbn Chna Abstract In vew of the problems of nonlnear feature extracton n face recognton a new algorthm of orthogonal optmal dscrmnant vectors and a new algorthm of statstcally uncorrelated optmal dscrmnant vectors n a kernel space were proposed based on neghborhood preservaton embeddng NPE Frst nonlnear kernel mappng was used to map the face data nto an mplct feature space Then the algorthm maxmzed nter-class neghborhood scatter nformaton whle mnmzng ntra-class neghborhood scatter nformaton n the kernel space whch helped to mprove ts dscrmnant ablty Fnally the kernel orthogonal preservng dscrmnant cmbeddng KONPDE algorthm and the kernel uncorrelated neghborhood preservng dscrmnant embeddng KUNPDE algorthm were obtaned by constrantng the base vectors orthogonal and uncorrelated respectvely Also the general theorem for solvng the base vectors of the above two algorthms and the dervatons of the algorthms were specfcally ntroduced Experments on Yale and PIE demonstrate the effectveness of the algorthms and show that these algorthms can reduce the dmensons of the data and mprove the dscrmnant ablty Keywords manfold learnng face recognton embeddng algorthm kernel space neghborhood preservng embeddng NPE 3 locally lnear embeddng LLE 1 localty preservng projectons LPP 4 Laplacan egenmap LE AA04Z E-mal luguanqun@ hrbeu edu cn E-mal zrbzrb@ hrbeu edu cn SVM KNPE kernel NPE 5 KLPP kernel LPP 6 LPP NPE LDE 7

2 7 939 LSDA 8 MFA 9 ANMM 10 NPDE 11 M w = I - W w T I - W w M b = I - W b T I - W b NPDE Deng Ca 12 LPP ONPE 13 OLSDA 14 OMFA 15 XM w X T V = λxm b X T V 3 2 NPDE 15 MFA NPDE 2 kernel orthogonal neghborhood preservng dscrmnant embeddng KONPDE kernel X X uncorrelated neghborhood preservng dscrmnant embeddng KUNPDE NPE V X = x 1 x 2 x n = v 1 v 2 v d Z = V T X Z = z 1 z 2 z n NP- DE Σ z - Σ W w j z j 2 j V = mn = Σ z - Σ W b jz j 1 NPE NPDE X = x 1 x 1 x n Y = y 1 y 2 y n V X Y Y = V T X NPE k V x 1 x 2 x n x α V W = Σ n α x = X α = 1 NPE mnσ y - Σ w j y j 2 = mn V T X I - W 2 = j mntr V T XMX T V 1 M = I - W T I - W d V T XX T V = I α 1 α 2 α d NPE KM w Kα = λkm b Kα 6 NPDE 3 NPDE V opt = mn Φ Vw Φ V b = mn VT X I - W w 2 V T X I - W b 2 = mn tr VT XM w X T V tr V T XM b X T V 2 mn VT X I - W w 2 V T X I - W b 2 = mn tr VT X M w X T V tr V T X M b X T V 4 K = k x x j = X T X 4 mn tr αt KM w Kα tr α T KM b Kα Φ V W Φ V b 2 W w 2 W b 1 V V T = I NPDE dst z z j = V T x - x j = 5 槡 x - x j T V V T x - x j = x - x j

3 Z 2 KM b K -1 KM w Kα k - KM b K -1 CT 槇 k-1 μ k-1 = 2λα k j E z - 13 E z z j - E z j = v T S t vj = 0 j S t = Σ n I - CT 槇 k -1 Q k -1-1 T T x t - m x - m T k -1 C KM 槇 b K -1 KM w Kα k = = λkm b Kα k 14 = 1 X I - ee T /n X T X G X T 7 P = I - CT 槇 k - 1 Q k T T k - 1 C槇 KM b K PKM w Kα k = λkm b Kα k A = α 1 α 2 α d x z l = Σ n α T j K j v k T Cv 1 = v k φ T Cv 2 = = v k T Cv k - 1 = 0 α T k 槇 Cα 1 = α T k 槇 Cα 2 = = α T k 槇 Cα k - 1 = 0 C = I 槇 C = k C = S t C 槇 = KGK Yale PIE α 1 KM w Kα = λkm b Kα k - 1 k x y = exp - x - y 2 /σ α T k = α T 槇 k Cα 2 = = α T 槇 k Cα k - 1 = 0 σ = k Γ k α k 2KM w Kα k - 2λKM b Kα k - μ 1 槇 Cα 1 - μ k-1 槇 Cα k-1 = α T 槇 j C KM b K -1 j =1 k -1 μ 1 α T 槇 j C KM b K -1 Cα 槇 1 + μ k-1 α T 槇 j C KM b K -1 Cα 槇 k-1 = 2α T j Q k - 1 = T T k - 1 槇 C KM b K -1 KM w Kα k 槇 C KM b K CT 槇 k - 1 k - 1 Q j = α T 槇 C KM b K - 1 Cα 槇 j T k - 1 = α 1 α k - 1 μ k - 1 = μ 1 μ k Q k-1 μ k-1 = 2T T k-1 槇 C KM b K -1 KM w Kα k 11 μ k - 1 μ k-1 = 2 Q k-1-1 T k-1 槇 C KM b K -1 KM w Kα k 9 KM b K l = 1 2 d z l z l 4 PCA PKM w Kα k = λkm b Kα k P = I - CT 槇 k - 1 Q k T T 槇 k - 1 C KM b M - 1 T k - 1 = α Yale α k - 1 Yale α T KM b Kα = I 5 20 Γ k = α T k KM w Kα k - λ α T k KM b Kα k - 1 μ 1 α T 槇 k Cα 1 μ 2 α T 槇 k C - α 2 - Lμ k -1 α T 槇 k Cα k Yale 2 NPE NPDE 1 LPP NPE NPDE ONPE Table 1 Fg j = 1 Yale Some example mages from ORL database Yale Best recognton rate and dmenson of dfferent methods on Yale database /% LPP NPE ONPE NPDE KUNPDE KONPDE

4 7 941 KONPDE KUNPDE Fg 3 3 PIE Some example mages from PIE database Fg 2 2 Yale Recognton rate vs dmenson on Yale database KUNPDE KONPDE LPP NPE ONPE NPDE PIE PIE PIE PIE PIE = Fg 4 Recognton rate vs dmenson on PIE database PIE Table 2 Best recognton rate and dmenson of dfferent 2 LPP NPE methods on PIE database NPDE ONPE 4 NPE NPDE /% KUNPDE LPP KONPDE 65 NPE 2 ONPE LPP NPE NPDE ONPE PIE NPDE KUNPDE ONPE KONPDE LPP NPE LPP NPE ONPE 5 NPDE NPE NPDE LPP NPE NPE KUNPDE KONPDE KUNPDE KONPDE Yale PIE

5 CAI D HE X ZHOU K HAN J et al Localty senstve dscrmnant analyss C / /Proceedngs of the 20th Internatonal Jont Conference on Artfcal Intellgence Hydera- bad Inda YAN Shucheng XU Dang ZHANG Benyu et al Graph embeddng and extensons a general framework for dmen- 1 ROWEIS S T SAUL L K Nonlnear dmensonalty reducton by locally lnear embeddng J Scence BELKIN M Laplacan egenmaps for dmensonalty reducton and data representaton J Neural Computaton HE Xaofe CAI Deng YAN Shucheng ZHANG Hongjang Neghborhood preservng embeddng C / / Tenth IEEE Internatonal Conference on Computer Vson Bejng Chna HE Xaofe YAN Shucheng Face recognton usng Laplacanfaces J IEEE Trans on Pattern Analyss and Machne Intellgence neghborhood preservng projectons for face recognton J Acta Electronca Snca KSLPP J ZHU Le ZHU Shanan KSLPP new algorthm for face recognton J Jorunal of Zhejang Unversty Engneerng Scence CHEN H Z CHANG H W LIU T Local dscrmnant embeddng and ts varants C / /2005 IEEE Computer Socety Conference on Computer Vson and Pattern Recognton San Dego USA sonalty reducton J IEEE Trans on Pattern Analyss and Machne Intellgence WANG Fe WANG Xn ZHANG Daoqang et al Margn face A novel face recognton method by average neghborhood margn maxmzaton J Pattern Recognton HAN P Y JIN A T B ABAS F S Neghborhood preservng dscrmnant embeddng n face recognton J Vs Commun Image R CAI Deng HE Xaofe HAN Jawe et al Orthogonal Laplacanfaces for face recognton J IEEE Transactons on Image Processng J TAO Xaoyan JI Hongbng JING Zhhong Orthogonal J PANG Yanwe YU Nengha SHEN Daoy et al Kernel neghborhood preservng embeddng algorthm for face recognton J Journal of Xdan Unversty Natural Scence JIN Y RUAN Quq Orthogonal localty senstve dscrmnant analyss for face recognton J Journal of Informaton Scence and Engneerng MFA MFA J YU Yaolang ZHANG Lmng Orthogonal MFA and uncorrelated MFA J Pattern Recognton and Artfcal Intelgence